The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°
Given,
A spring is attached at one end to support B and at the other end to collar A.
Part A: Reference angle (θ) = 28°
We have to find out the distance of point A to point B.
Adjacent = 3 ft (given)
Apply the trigonometry function to find AB
cos θ = adj / hypotenuse
Substituting all the values ,
cos 28°= 3/AB
AB = 3/cos 28°
AB = 3.4 ft (nearest tenth of a foot)
Part B:
It is given that Distance from point A to point B is 5.2 feet
We have to calculate the Value of θ
adjacent = 3 ft
hypotenuse = AB = 5.3 ft
To find θ , We will again apply the trigonometry function
cos θ = adjacent/hypotenuse
Substituting all the given values
cos θ = 3/5.3
θ = cos⁻¹ ( 3 / 5.3)
θ = 54.8°
That is,
The length of point A to point B is 3.4 feet
The value of θ is 54.8°
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“The sum of three and a number, divided by three, is five”
I need help again due tomorrow
Answer: The number is 12
Step-by-step explanation:
Let x= the number that is unknown
The sum of three and a "number"= 3+"x"
Divided by three, means that x+3 is divided by 3
Is five, means that (x+3)/3=5
Algebra:
[tex]\frac{x+3}{3}=5[/tex]
Multiply by 3 to arrive at x+3=15
Subtract both sides by 3, then x=12
The yearly profits of a company is $25,000. The profits have been decreasing by 6% per year.
Part A: Write an exponential function that represents this scenario. Format your answer like: A(t)=a\left(1\pm r\right)^{t}A(t)=a(1±r)
t
An Exponential Function that can depict this situation is [tex]A(t) = 25000(0.94)^{t}[/tex]
What is an Exponential Function?
An exponential function is a mathematical function of the following form: [tex]f(x)=a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula [tex]y=a(1-r)^{x}[/tex] wherein y is the final amount, a is the original amount, r is the decay factor, and x(or t) is the amount of time that has passed.
Given :
The initial amount is 25,000, and the rate of decay is 6%, or 0.06.
Write the exponential Decreasing function.
[tex]A(t) = a(1-r)^{t}[/tex]
Substitute 25,000 for a and 0.06 for r.
[tex]A(t)=25,000(1-0.06)^{t} = 25,000(0.94)^{t}[/tex]
Hence , the Situation can be represented by [tex]A(t) = 25000(0.94)^{t}[/tex]
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Please help me.
Prove that if a + b > 100, a, b, or both must be greater than 50
Answer:
Step-by-step explanation:
To prove this statement, we can use the contrapositive. The contrapositive of the statement "If a + b > 100, then a, b, or both must be greater than 50" is "If a and b are both less than or equal to 50, then a + b is less than or equal to 100."
To prove the contrapositive, we must show that if a and b are both less than or equal to 50, then a + b is indeed less than or equal to 100. This is easy to do, because if a and b are both less than or equal to 50, then the largest possible value for a is 50 and the largest possible value for b is 50. Therefore, the largest possible value for a + b is 50 + 50, which is equal to 100.
Since the contrapositive is true, it follows that the original statement must also be true. Therefore, we have proven that if a + b > 100, then a, b, or both must be greater than 50.
PLEASE HELP GIVING BRAINLIEST!!!!!!!!!!!!!!!!!!!!
Select all that apply. Which equations could you use to solve the following problem? Seventy-eight is 55% of what number? p = (0.85)78 = 78 = (0.55) w =
Answer:
x/78 = 55/100
Step-by-step explanation:
Solve for x.
Thank you
Answer:
12
Step-by-step explanation:
The measure of each interior angle is [tex]\frac{180(8-2)}{8}=135^{\circ}[/tex].
[tex]\implies 135=9x+27 \\ \\ 15=x+3 \\ \\ x=12[/tex]
What is the probability of landing on a 5 and then landing on an even number?
Write your answer as a percentage rounded to the nearest tenth.
The probability of landing on a 5 and then landing on an even number is 8.3%.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
The number of 5 on the dice is one.
Probability is the ratio of the number of favorable outcome to the total number of outcome.
The number of faces of dice is 6.
The probability of getting 5 is 1/6.
The even faces on the dice are 2, 4, 6.
The number of even number faces is 3.
The probability of getting even number is 3/6 = 1/2.
The probability of two independent event is the product of the probability of the events.
Therefore, the probability is (1/6) × (1/2)
= 1/12
= 0.083
= 8.3%
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Each student wrote a two-step equation. Peter wrote the equation 5x − 4 = 16, and Andres wrote the equation 20x − 16 = 64. The teacher looked at their equations and asked them to compare them. Complete the description of one way in which the equations are similar.
To get Andres' equation, you can multiply every number in Peter's equation by what?
Answer: 4
Step-by-step explanation:
This is Peter equation 5x − 4 = 16
This is Andres equation 20x − 16 = 64
To get from Andres's equation, you multiply every number in Peter's equation by 4
5x times 4 = 20x
-4 times 4 = -16
16 times 4 = 64
If you can, please give me a Brainliest; thank you!
Answer:
4
Step-by-step explanation:
So if you look closely at the equations, you will find out that Andres equation is the same as Peter but 4 times bigger
5x-4=16
20x-16=64
20x-16=64/5x-4=16
= 4
Now let's check
4(5x-4)=4(16)
Therefore, 4 is the answer.
Andres equation is 4 times as big as Peter (but it has the same result)
Please, give me the brainliest if you can
Through a given point not contained in a given line, there exists ___ ___ line parallel to the given line. (two words)
There is ONLY ONE __ line parallel to the provided line that passes through a certain point that is not contained in the supplied line.
What do parallel lines mean?Parallel lines are any two or more lines that are in the same plane but never cross one another ( never intersect). Both have the same slope and are equally far from one another.
We have a line and a point outside the line;
from that point, we can generate many lines, but only one of those lines will be parallel to the line as it is. From a point, we can make many lines, but that point can only create one line that will be parallel to a given line.
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If f(x)=x^2-3x-2f(x)=x
2
−3x−2, then what is the remainder when f(x)f(x) is divided by x-7x−7?
When x²-3x-2 is divided by x-7, the remainder is 26, and the quotient is x+4.
What is polynomial?Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Here
f(x)=x²-3x-2
divisor=x-7
When x²-3x-2 is divided by x-7,
The quotient is x+4.
The remainder is 26.
The remainder will be 26 when x²-3x-2 is divided by x-7 and the quotient will be x+4.
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Henry took 42.7 minutes to complete an exam Laticia took 28.7 minutes to complete the same exam who completed their exam first
Answer:
Unless these took place in different time periods, Laticia did first.
Step-by-step explanation:
28.7 < 42.7
Use the Distributive Property to express 64 + 24
Using the the Distributive Property to express 64 + 24 is 88.
In mathematics, what is a distributive property?This property states that multiplying the sum of two or more addends by a number produces the same result as multiplying each addend separately by the number and then adding the products together.
When you multiply a value by a sum, the distributive property of multiplication over addition is used. For instance, suppose you want to multiply 5 by the sum of 10 + 3. When we have similar terms, we usually add the numbers first and then multiply by 5. 5(10 + 3) = 5(13) = 65.
In this case, 64 + 24 will be;
= 8(8 + 3)
= 88
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You're given AIKJ with m/JIK = 53°, m/IKJ = (82-5x), and m/KJI = (7z+24)°. What is mZIKJ? Your final answer might not look to
scale. Do NOT round your answer.
Angle ∠IKJ is 29.5 degrees for triangle IKJ.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given triangle is IKJ.
The angles are given as follow.
∠JIK = 53°,
∠IKJ = (82-5x), and
∠KJI = (7x+24)°.
We need to find the angle ∠IKJ .
By angle sum property of triangle, the sum of three angles is 180 degrees.
∠JIK+∠IKJ+∠KJI = 180
Fifty three plus eighty two minus five times of x plus seven times of x plus twenty four equal to one hundred and eighty.
53+82-5x+7x+24=180
Add the like terms
159+2x=180
One hundred fifty nine plus two times of x equal to one hundred eighty.
subtract 159 on both sides
2x=21
Divide both sides by 2.
x=10.5
So ∠IKJ is 82-5(10.5)=29.5 degrees.
Hence, the value of angle ∠IKJ is 29.5 degrees.
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Literal Equations
help asap !!
Answer:
Step-by-step explanation:
P = F/a
Pa = F
a = F/P
Answer:
a = [tex]\frac{F}{p}[/tex]
Step-by-step explanation:
P =[tex]\frac{F}{a}[/tex] multiple both sides by a
aP = [tex]\frac{F}{a}[/tex] [tex]\frac{a}{1}[/tex] On the right side of the equal sign, the a's cancel each other out
aP = F Divide both sides by P
[tex]\frac{aP}{P}[/tex] = [tex]\frac{F}{P}[/tex] The P's cancel out on the left side of the equal sign.
a = [tex]\frac{F}{P}[/tex]
Your family goes to a Southern-style restaurant for dinner. Some order chicken dinner for $14 each and some order the steak dinner for $17 each. If the total bill came to $99, how many people ordered dinner?
People in my family ordered 1 chicken dinner and 5 steak dinner.
There are total 6 peoples in a family.
Let's x number of people order chicken dinner
and y number of people order steak dinner.
Here we have to use concept of linear equation.
we have to make 2 linear equation and solve them to get the value.
sum of number of people is 6.
[tex]x + y = 6[/tex] --- i
total bill came to $99.
1 chicken dinner takes $14.
So x chicken dinners takes x*14
1 steak dinner takes $17.
So y steak dinners takes y*17.
Sum of both dinners price
[tex]x*14+y*17 = 99[/tex] -- ii
From equation i x = 6 - y.
put value of x in equation ii.
(6-y)*14+y*17 = 99
84-14*y+17*y = 99
3*y = 99-84
3*y = 15
y = 5
x = 6-5 = 1.
So 1 people ordered chicken dinner and 5 people ordered steak dinner.
Given Question is incomplete Complete Question here
Your family goes to a southern style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14 and some order the steak dinner for $17. If the total bill was $99 l, how many people ordered each dinner?
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Jessica deposits her summer babysitting earnings, $600, in a savings account. How many years will it take her to earn $150 in interest at a simple annual rate of 5%? Enter the correct number in the formula.
150 = (600) (.05) (?)
this is a middle school question not high school sorry
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 150\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 150 = (600)(0.05)(t) \implies \cfrac{150}{(600)(0.05)}=t\implies 5=t[/tex]
47.5 min to jog 5 mi, min to jog 11 mi
Answer:
104.5 min
Step-by-step explanation:
47.5:5=x:11
1. Simplify
9.5:1=x:11
2.Solve
x=104.5
Factor the following expression.
5x5 - 3x² - 10x³ +6
(x2 – 2) (5x3 – [?]
Answer:
(x²-2) (5x³-3)
Step-by-step explanation:
rearrange terms
5x⁵-10x³-3x²+6
find one factor
(x²-2) (5x³-3)
Here is a solid prism.
7 cm
-5 cm-
11 cm-
Work out the volume of the prism.
cm
20 cm
Diagram NOT
accurately drawn
Answer:
1180 cm³
Step-by-step explanation:
You want the volume of a prism with an L-shaped base. It is 20 cm between bases. The outside dimensions of the L are 7 cm high by 11 cm wide; the inside dimensions are 3 cm high by 6 cm wide.
Volume formulaThe formula for the volume of a prism is ...
V = Bh
where B is the area of the base, and h is the distance between them. We know h, but we need to find B.
Base areaThe area of an L-shape is the area of the rectangle with the outside dimensions, less the area of the rectangle with the inside dimensions.
A = LW -lw
A = (11 cm)(7 cm) -(6 cm)(3 cm) = 77 cm² -18 cm² = 59 cm²
VolumeUsing the above formula, the volume is ...
V = (59 cm²)(20 cm) = 1180 cm³
The volume of the prism is 1180 cubic centimeters.
__
Additional comment
The dimensions of the inside of the L are found by subtracting the given width of the legs from the outside dimensions.
7 cm -4 cm = 3 cm . . . . inside height
11 cm -5 cm = 6 cm . . . . inside width
You can also find the area of the base by extending one or the other of the lines to divide it into two rectangles. Extending the vertical line makes the left rectangle 7 cm high by 5 cm wide. The right rectangle is 4 cm high by 6 cm wide. Then the area is 7·5 +4·6 = 35+24 = 59, as above.
Raquel wants to buy a concert ticket online. Raquel has a coupon code to discount the cost of the concert ticket. The cost of the concert ticket online has been found to be t-.25t + 15, where t the cost of the ticket in dollars.
By what percent is the ticket cos being discount ?
How much is the flat booking fee ?
Answer:
the percent being discounted is 25% and the flat booking fee is 15
Step-by-step explanation:
t is the cost of the ticket. -.25t is the 25% coupon being taken off. The 15 is the booking fee.
Help mehhhhhhh please
Answer:
Jordan
Step-by-step explanation:
The composite number was 21.
21 can be divided by 3 and 7.
Answer: Jordan.
Step-by-step explanation:
Prime numbers are special numbers that have no divisors other than itself and [tex]1[/tex]. Prime numbers are observed in the lists created by the students.
Compound numbers are numbers that can be written as the product of at least two prime numbers. When we look at Jordan's list, we will see that the number [tex]21[/tex] breaks this rule. Because the number [tex]21[/tex] is the product of both prime numbers [tex]3[/tex] and [tex]7[/tex]. It is not a prime number. It is a composite number.
How many ways can you answer a 5 multiple choice question test, where there are 4 choices for each question
There are 1024 ways to answer the 5 multiple choice question having 4 options
What is permutation ?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. A permutation is a term that describes the variety of possible arrangements or orders of objects.
We have 5 multiple choice questions.
And we are given four options to solve the question
Repeating is permitted (you can answer "c" on all of the questions if you want to)
So ,
We will use permutation to solve the question
[tex]n^{r}[/tex]
r is number of questions = 5
n is number of choices = 4
[tex]4^{5}[/tex] = 4×4×4×4×4 = 1024
There are 1024 ways to answer the 5 multiple choice question having 4 options
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(-5)+8 x 2 please help
Answer:
11
Step-by-step explanation:
-5 + 8 x 2
Do multiplication first because PEMDAS -5 + 16
Then add: 11
Answer:
11
Step-by-step explanation:
8x2 = 16
-5+16 = 11
If you do a question like this always use PEMDAS. Do it in order.
P arenthesis
E exponents
M ultiplcation
D ivision
A ddition
S ubtraction
Pick the most affordable gift (select the cheapest one): A) Laptop that originally cost $2399.99, has a discount of 40% and a sales tax of 8.2% B) A smart TV that originally cost $1799.99, has a discount of 10% and a sales tax of 4.5% C) A brand new Iphone that regularly costs 1699.99, has a 5% discount and a sales tax of 6.8% D) A GeForce 3090 RTX graphics card costs $2199.99, you have a coupon for $500 off. The sales tax is 7.5% A D B&C C B C&D
Option A) Buying a laptop will be most affordable among all the options as per the Selling price with Sales tax included.
What is Selling Price and Discount and Sales Tax?The selling price is the price at which a thing is sold. Typically, it is identified as SP. also known as a selling price on occasion.
Shop owners essentially mark this as a promotional item to give discounts to customers in a way that,
Discount equals Marked Price - Selling Price, and Discount Percentage is (Discount/Marked price) times 100.When a product is sold to a buyer, the government levies sales tax (abbreviated as ST). This tax will be collected by the merchant and paid to the government. As a result, it is added to the bill after being charged on the item's selling price.
Sales tax = Tax% of Bill AmountTotal Bill = Cost of the Item + Sales TaxFor Laptop,
Selling Price = (100-40)% of 2399.99
= 60% of 2399.99 = $ 1439.99
Total bill = 1439.99 + 8.2% of 1439.99
= 1439.99 + 118.08 = $ 1558.07
For Smart TV,
Selling Price = (100-10)% of 1799.99
= 90% 0f 1799.99 = $ 1619.99
Total bill = 1619.99 + 4.5% of 1619.99
= 1619.99 + 72.9 = $ 1692.89
For Iphone,
Selling Price = (100-5)% of 1699.99
= 95% 0f 1699.99 = $ 1614.99
Total bill = 1614.99 + 6.8% of 1614.99
= 1614.99 + 109.82 = $ 1724.81
For GeForce RTX 3090 Graphics Card,
Selling Price = 2199.99 - 500 = $ 1699.99
Total bill = 1699.99 + 7.5% of 1699.99
= 1699.99 + 127.5 = $ 1827.49
Total bill
Graphics Card > Iphone > Smart TV> Laptop.
Option A) Buying a laptop will be most affordable among all the options.
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need the answer for my math homework
[tex]\cfrac{2}{3}-\cfrac{5}{12}\implies \cfrac{(4)2~~ - ~~(1)5}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{8~~ - ~~5}{12}\implies \cfrac{3}{12}\implies \cfrac{3\cdot 1}{3\cdot 4}\implies \cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{4}{5}+\cfrac{11}{12}\implies \cfrac{(12)4~~ + ~~(5)11}{\underset{\textit{using this LCD}}{60}}\implies \cfrac{48~~ + ~~55}{60}\implies \cfrac{103}{60}\implies 1\frac{43}{60}[/tex]
The square root of (-5x)^3, for which values of x does this expression make sense?
Answer: Yes it does, it is -125x to the power of 3.
Step-by-step explanation:
Answer:MONKEY
Step-by-step explanation:
CAUSE I SAID DO
In 1983, a pair of jeans cost $66.35. If a pair of jeans costs $118.10 today, what is the CPI? a. 152 b. 156 c. 178 d. 184 Please select the best answer from the choices provided A B C D
The value of CPI will be 178.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In 1983, a pair of jeans cost $66.35.
And, A pair of jeans costs $118.10 today.
Now,
Since, In 1983, a pair of jeans cost $66.35.
And, A pair of jeans costs $118.10 today.
Hence, The value of CPI will be;
CPI = 118.10 × 100 / 66.35
= 11810 / 66.35
= 178
Thus, The value of CPI will be 178.
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if an analyst is studying the wait times at a clinic and the only list of patients available is on hard copy, which sampling technique is the easiest to use?
Sampling technique is the easiest to use here is systematic sampling.
Given :
if an analyst is studying the wait times at a clinic and the only list of patients available is on hard copy .
The sampling technique in this scenario is used is systematic sampling.
Systematic sampling :
Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval.
k = N/n
where
k = systematic sampling interval
N = population size
n = sample size.
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What is the area of AFGH?
-10 -8 -6
H
Area =
-4 -2
square units
104
-8
6
4
2
0
2
-4
-6
-8
-10
4
6
8
00
F
X
10
G
Answer:
-2 = x 4-2 square units
Step-by-step explanation:
sum = as per as chart
Please answer! Thank youuu
Answer:
36%
Step-by-step explanation:
People with size 7 shoes = 5
People with size 7½ = 7
People with size 8 = 9
People with size 8½ = 3
People with size 9 = 1
To find out the total, you have to add all the people up:
5 + 7 + 9 + 3 + 1 = 25
The total amount of students = 25
Since you're trying to find the percentage of students who have a shoe size of 8, you have to look at how many people have that size:
People with size 8 = 9
To find out the percentage you do:
9/25 × 100 = 36%
Therefore 36% of students have a shoe size of 8
:)
Solve the following equation for x:
3(x+5) = 1/9
8
4
-8
None of these choices are correct.
The solution to the linear equation 3(x + 5) = 1/9 is
x = -4 26/27.
The correct answer is option D; None of these choices are correct.
How to solve linear equation?3(x + 5) = 1/9
open parenthesis
3x + 15 = 1/9
Substract 15 from both sides
3x = 1/9 - 15
3x = (1-135)/ 9
3x = -134/9
divide both sides by 3
x = -134/9 ÷ 3
Multiply by the reciprocal of 3
x = -134/9 × 1/3
= -134/27
x = -4 26/27
Therefore, -4 26/27 is the solution that satisfies the equation 3(x + 5) = 1/9
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