The length of one leg of the triangle is equal to 7 units.
How to determine the length of one leg of the triangle?Based on Pythagorean theorem, the length of sides of a right-angled triangle are always in the ratio 1 : 1 : √2, which can be rewritten as follows;
x : x: x√2.
Where:
x represent the length of sides (one leg) of a right-angled triangle.
From this 45-45-90 triangle, we can determine the length of one leg of the triangle as follows:
x = 1/√2 × (7√2)
x = 7 units.
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Complete Question:
The hypotenuse of a 45°-45°-90° triangle measures 7√2 units. what is the length of one leg of the triangle?
Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean μ = 8544 gallons and standard deviation σ = 12 gallons. A simple random sample of n = 20 tanks will be selected. Find the z-score corresponding to a sample mean capacity for 20 tanks of 8550. Round your answer to three decimal places. (Example: 0.398)
The z-score corresponding to a sample mean capacity for 20 tanks of 8550 is 2.238.
To find the z-score corresponding to a sample mean capacity for 20 tanks of 8550, we need to use the formula for the z-score:
z = (x - μ) / (σ / √n)
Where:
x = sample mean capacity
μ = population mean capacity
σ = population standard deviation
n = sample size
Given:
x = 8550, μ = 8544, σ = 12 and n = 20
Substituting these values into the formula:
z = (8550 - 8544) / (12 / √20)
z = 6 / (12 / √20)
z = 6 / (12 / 4.472)
z = 6 / 2.683
z = 2.238
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Graph g(x) the transformation of f(x)=x2 translated up 4 unit
If Graph g(x) the transformation of f(x)=x² then the graph of function g(x) is x²+4
To graph the transformation of the function f(x) = x² translated up 4 units, we need to add 4 to the function.
The new function, g(x), can be defined as g(x) = f(x) + 4.
Start with the graph of the original function f(x) = x²
Shift the graph vertically upward by 4 units.
To do this, for each point (x, y) on the graph of f(x), plot a new point (x, y + 4) on the graph of g(x).
This means that every y-coordinate is increased by 4 units.
g(x)= x²+4
Hence, the red line in the graph represents f(x) and blue line in graph represents the g(x)
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There is a jar in the cabinet by the refrigerator. If Kenna pours 114 ounces of water into the jar 3 times to fill it, how many quarts of water does it take to fill the jar? (Round to then nearest whole number)
Answer:
Since 1 fluid ounce is equal to 0.03125 quarts, we can convert the volume of water poured into the jar from ounces to quarts:
114 ounces x 0.03125 quarts/ounce = 3.5625 quarts
Therefore, Kenna pours 3 x 3.5625 = 10.6875 quarts of water to fill the jar three times. Rounding to the nearest whole number, we get 11 quarts.
So it takes 11 quarts of water to fill the jar.
Use limits to find the area of the region between the graph of y=x² +1
and the x-axis on the interval [2, 4], or f(x²+1) dx
Answer: To find the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4], we can integrate the function f(x) = x^2 + 1 with respect to x over the given interval. The definite integral represents the area under the curve between the specified x-values. Here's how to calculate it using integration:
∫[2,4] (x^2 + 1) dx
To integrate this function, we apply the power rule for integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1), where n is any real number except -1.
∫(x^2 + 1) dx = [(x^3)/3 + x] + C
Now, we can evaluate the definite integral over the interval [2, 4]:
[(4^3)/3 + 4] - [(2^3)/3 + 2]
= (64/3 + 4) - (8/3 + 2)
= (64/3 + 12/3) - (8/3 + 6/3)
= (76/3) - (14/3)
= 62/3
Therefore, the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4] is 62/3 square units.
Step-by-step explanation:
what should be subtracted from 7/12+7/8 to obtain the multiplicated inverse of (4/3-4/9)
To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.
First, let's find the multiplicative inverse of (4/3 - 4/9):
Multiplicative inverse = 1 / (4/3 - 4/9)
To simplify the expression, we need a common denominator:
Multiplicative inverse = 1 / ((12/9) - (4/9))
= 1 / (8/9)
= 9/8
Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:
Subtracted value = (7/12 + 7/8) - (9/8)
To perform this calculation, we need a common denominator:
Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)
= (14/24 + 21/24) - (9/8)
= 35/24 - 9/8
To simplify further, we need a common denominator:
Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)
= 35/24 - 27/24
= 8/24
= 1/3
Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The
equation 200e0.08350 represents the situation, where t is the number of years the money has been invested. About
how long has the money been invested? Use a calculator and round your answer to the nearest whole number.
O 5 years
O 7 years
O 19 years
O 22 years
A population has mean 12 and standard deviation 4. Round the answers to two decimal places as needed. Find the z-score for a population value of 21.
To find the z-score for a population value of 21, we can use the formula:
z = (x - μ) / σ
where:
x = population value
μ = mean of the population
σ = standard deviation of the population
In this case, x = 21, μ = 12, and σ = 4.
Substituting the values into the formula:
z = (21 - 12) / 4
z = 9 / 4
z = 2.25
Therefore, the z-score for a population value of 21 is 2.25.
Note:
I hoped this helped in any kind of way.
abs(2x+5)+abs(3x-1)=10
Answer:
Step-by-step explanation:
x=6/5,−4
Decimal Form:
x=1.2,−4
Mixed Number Form:
x=1 1/5,−4
A car owner pays an annual premium of $780 for automobile insurance, including liability coverage of up to $100,000. The car owner pays this for five years without needing to file a single claim. Then the car owner causes an accident for which the other driver is claiming $32,000 in damages. How much more expensive were the costs of the accident than what the car owner paid in premiums?
$3,900
$28,100
$35,900
$100,000
The correct answer is $28,100.
To calculate the difference between the costs of the accident and the premiums paid by the car owner, let's break down the expenses step by step:
(1) Annual Premium: The car owner pays an annual premium of $780 for automobile insurance. Over five years, the total premium paid is $780 * 5 = $3,900.
(2) Liability Coverage: The liability coverage provided by the insurance is up to $100,000. However, the other driver is claiming $32,000 in damages. Therefore, the insurance will cover the full amount of $32,000.
(3) Difference in Costs: To find the difference between the costs of the accident and the premiums paid, we subtract the insurance coverage from the total premium paid. In this case, the difference is $32,000 - $3,900 = $28,100.
Therefore, the costs of the accident were $28,100 more expensive than what the car owner paid in premiums.
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Wonwoo has 3 cupcakes. Grace gives 2 cupcakes to Wonwoo and Wonwoo gives 1 cupcake to Grace. Later, Grace's friend Lois and Seeun each gives 4 cupcakes to Wonwoo. How many cupcakes does Wonwoo have now?
Answer:
After Grace gave 2 cupcakes to Wonwoo, he had a total of 5 cupcakes. However, after he gave 1 cupcake to Grace, he was left with 4 cupcakes again. But then, things took a turn for the better when Lois and Seeun each gave him 4 cupcakes. This means that Wonwoo now has a total of 12 cupcakes!
Step-by-step explanation:
I believe this is right; please tell me if it is not.
Express the graph shown in color using interval notation. Also express the graph as an inequality involving x.
The interval notation of the number line is [-3, ∝) while that of the inequality is called x >= 3
What is the interval notation?One can use interval notation to represent real numbers that are continuous by specifying the values that define their boundaries. Written intervals appear somewhat akin to ordered pairs.
The way to know the interval notation of the graph is:
Based on the number line in the question, one can see:
The endpoint is a closed line at x = -3The arrow points is one that is to the rightThe rule that applies is that a closed line tells us that the number at that endpoint is one that is part of the solution set.
So this tells us that the interval notation of the number line is [-3, ∝). When depicted as an inequality, One can have x >= 3
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The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
a. bus
b. car
c. subway
d. train
Answer: C
Step-by-step explanation:
For box and whiskers plot the box is where the majority of the data is. the whiskers(the lines on both sides will tell you where the range of numbers lie)
The middle line in the box is the median number.
The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)
You want the majority of the data to be less than 30, which is subway. C
1. The list below shows the ages of the first 20 customers at a new computer game
store.
6, 7, 9, 10, 14, 15, 16, 17, 20, 26, 26, 29, 31, 34, 35, 38, 40, 51, 59, 67
a) Decide what class intervals to use, and then create a frequency table for the
ages. (4 points: 2 points for intervals, 2 points for frequencies)
Age
Frequency
The class intervals to use for the given data is 10.
What is a class interval?The class interval is the difference between the upper class limit and the lower class limit. Class interval represents the width of each class in a frequency distribution
What is a frequency?The frequency of a class interval is the number of observations that occur in a particular predefined interval.
From the given data the prepare a table for age and frequency
[tex]\begin{tabular}{c | l} Age & Frequency \\ \cline{1-2} 0-10 & 4 \\ 11-20 & 5 \\ 21-30 & 5 \\ 31-40 & 5 \\ 41-50 & 0 \\ 51-60 & 2 \\ 61-70 & 1 \end{tabular}[/tex]
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In the middle of 3 consecutive numbers is x. Determine the numbers if their sum is 51
Answer:
16, 17, 18----------------------
If the middle number is x, the other numbers are x - 1 and x + 1.
They sum to 3x and it is equal to 51:
3x = 51x = 17The numbers are 16, 17 and 18.
Consider the following symbolic logic statement: ¬ (∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
a) Translate the statement into English using proper syntax and semantics.
b) Identify and explain any potential ambiguities in the translated statement.
c) Rewrite the statement in a way that eliminates any ambiguities and maintains the original meaning.
The rewritten statement : "It is not the case that there exists an x for which P(x) and Q(x) are true, and for all y, if R(y) is true, then P(y) is true."
The symbolic logic statement: ¬(∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y)).
The statement can be translated as: "There does not exist an x such that P(x) and Q(x) hold true, and for all y, if R(y) is true, then P(y) is true."
Potential ambiguities in this statement can arise from the unclear precedence of logical operators, specifically the negation operator "¬" in relation to the existential quantifier "∃".
To eliminate ambiguities while maintaining the original meaning, we can add parentheses to make the precedence explicit: (¬(∃x)(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y)).
This ensures that the negation applies only to the existential quantifier, not to the entire conjunction.
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order from least to greatest -7, -8, -2, 6, | -11 |, - 11, -9, 4, 5
The given numerical data should be ordered from least to greatest as follows;
-11, -9, -8, -7, -2, 4, 5, 6, |-11|.
What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals.
In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).
Next, we would order or sort the given numerical data from least to greatest as follows;
-11, -9, -8, -7, -2, 4, 5, 6, |-11|.
Note: |-11| is an absolute value that equals to 11.
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PLEASE HELP ITS GEOMETRY
Answer:
[tex]slope_{UF}[/tex] = - [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = U (3, - 5 ) and ( x₂, y₂ ) = F (- 1, - 4 )
m = [tex]\frac{-4-(-5)}{-1-3}[/tex] = [tex]\frac{-4+5}{-4}[/tex] = [tex]\frac{1}{-4}[/tex] = - [tex]\frac{1}{4}[/tex]
Two lines intersect and create four angles one angle is 70 degrees the angle x and y are both linear angle pairs with 70 degrees the angles x is a vertical angle to 70 degrees find the degrees of the angles x and y and z.
Answer:
The angles x, y, and z are 70 degrees, 110 degrees, and 110 degrees, respectively.
Step-by-step explanation:
If one angle is 70 degrees, then its corresponding angle will also be 70 degrees. Therefore, the two linear angle pairs with 70 degrees are:
70 degrees and its corresponding angle (also 70 degrees)
x degrees and y degrees, where x and y add up to 180 degrees (because they are linear angle pairs)
Since x is a vertical angle to 70 degrees, it is also equal to 70 degrees. Therefore:
x = 70 degrees
y = 180 - x = 180 - 70 = 110 degrees
To find the angle z, we can use the fact that the sum of the angles around a point is 360 degrees. Since the two lines intersect and create four angles, the angles around the point where they intersect must add up to 360 degrees. Therefore:
z + 70 + 70 + 110 = 360
z + 250 = 360
z = 110 degrees
Therefore, the angles x, y, and z are 70 degrees, 110 degrees, and 110 degrees, respectively.
What is the quadratic equation??
Plsss reply I’ll mark as brainliest
Hello !
1. A quadratic equation results in the form: ax² + bx + c
2. Calculate the discriminant: Δ = b² - 4ac
3. Calculate x with the dicriminant: (-b ± √Δ) / 2a
Example:
3x² + 7x - 2 = 0 is a quadratic equation.
x = (-b ± √(b² - 4ac)) / 2a
= (-7 ± √(7² - 4*3*(-2))) / (2*3)
= (-7 ± √73)/6
What is the approximate value of θ if tan θ = 7/9
Answer:
37.9°-----------------------
Taking the inverse tangent (arctan) of the given ratio 7/9.
Use a calculator or trigonometric table to find:
θ ≈ arctan(7/9)The approximate value of θ is 37.9°.
What is the number of possible combinations of 10 men chosen from 26 men in the juror pool? Write your response in the form nCr.
The number of possible combinations of 10 men chosen from 26 men in the juror pool is, 44128260
Since, A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
We have to given that;
Total person = 26
Number of choose person = 10
Hence, The number of possible combinations of 10 men chosen from 26 men in the juror pool is,
⇒ ²⁶ C ₁₀
⇒ 26! / 10! 16!
⇒ 44128260
Thus, The number of possible combinations of 10 men chosen from 26 men in the juror pool is, 44128260
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Work out the perimeter of the shaded shape on the centimetre grid.
Give the answer in cm and no spam.
Answer:
The perimeter of this rectangle is 10 cm.
a straight line has an equation given by:
2y= 4x-5.
write down the gradient of the straight line
Step by Step Solution/ just copy and paste but if this is a test, the answer is 2.000
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*y-(4*x-5)=0
STEP
1
:Equation of a Straight Line
1.1 Solve 2y-4x+5 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2y-4x+5 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is -5/2 so this line "cuts" the y axis at y=-2.50000
y-intercept = -5/2 = -2.50000
Calculate the X-Intercept :
When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000
x-intercept = 5/4 = 1.25000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.500 and for x=2.000, the value of y is 1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.500 - (-2.500) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 4.000/2.000 = 2.000
Geometric figure: Straight Line
Slope = 4.000/2.000 = 2.000
x-intercept = 5/4 = 1.25000
y-intercept = -5/2 = -2.50000
Find the measure of w
Before an election,
33% said they would vote for Party A
10% said they would vote for Party B
15% said they would not vote.
These all voted as they said.
In the rest of the population 1/3
voted for Party A and 2/3 voted for Party B.
Who got the most votes?
You must show your working.
Given statement solution :- Party A received the most votes with a total of 47, compared to Party B's total of 38 votes.
Let's calculate the number of votes each party received based on the given information.
Assuming there is a population of 100 people (this is an arbitrary number chosen for ease of calculation), we can determine the number of votes for each party.
Percentage of people who said they would vote for Party A = 33%
Number of people who said they would vote for Party A = 33/100 * 100 = 33
Percentage of people who said they would vote for Party B = 10%
Number of people who said they would vote for Party B = 10/100 * 100 = 10
Percentage of people who said they would not vote = 15%
Number of people who said they would not vote = 15/100 * 100 = 15
Now, let's calculate the votes from the rest of the population (those who didn't state their voting preference).
Percentage of people who voted for Party A from the rest of the population = 1/3
Number of people who voted for Party A from the rest of the population = (1/3) * (100 - (33 + 10 + 15)) = (1/3) * 42 = 14
Percentage of people who voted for Party B from the rest of the population = 2/3
Number of people who voted for Party B from the rest of the population = (2/3) * (100 - (33 + 10 + 15)) = (2/3) * 42 = 28
Now, let's calculate the total votes for each party:
Total votes for Party A = votes from those who stated their preference + votes from the rest of the population
= 33 + 14 = 47
Total votes for Party B = votes from those who stated their preference + votes from the rest of the population
= 10 + 28 = 38
Therefore, Party A received the most votes with a total of 47, compared to Party B's total of 38 votes.
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express cos A as a fraction in simplest terms
12/13 is the value of cosA is in the triangle ABC
ABC is a right angle triangle
Angle B has a angle of 90 degrees
We know that the cosine function is a ratio of adjacent side and hypotenuse
The adjacent side of angle A is AB which we have to find
hypotenuse is 26
Cos A =AB/26
Let us find AB by using pythagoras theorem
10²+AB²=26²
100+AB²=676
Subtract 100 from both sides
AB²=576
Take square root on both sides
AB=√576
=24
Now plug in this value in cosA
CosA = 24/26
=12/13
Hence, the value of cosA is 12/13 in the triangle ABC
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Solve and explain please
Certainly! I'll be happy to solve and explain the given problem to you in a step-by-step manner.
In the given diagram, we have a triangle with two angles labeled as 4x° and (3x + 10)°. We need to solve for the value of x.
According to the properties of triangles, the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the following equation:
4x + (3x + 10) + 90 = 180
Let's simplify the equation:
4x + 3x + 10 + 90 = 180
7x + 100 = 180
Next, we'll isolate the variable term by subtracting 100 from both sides of the equation:
7x = 180 - 100
7x = 80
To solve for x, we'll divide both sides of the equation by 7:
x = 80 / 7
Now, let's calculate the value of x:
x ≈ 11.43
Therefore, the value of x is approximately 11.43.
Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.
4. **Suzie makes a purchase of $160 and is charged 7.85% for sales tax. What is the total cost of the purchase if Suzie charges it on a credit
card with a daily interest rate of 0.042% and pays the balance off at the end of 30 days? Round to the nearest cent
Hint: 1st, calculate the total cost of the purchase, which includes the sales tax. It is $160+($160 sales tax). Don't forget to change to
decimal before multiplying.
2nd, what will the interest per day be? You can find this by multiplying 0.042% (change to decimal first) by the total cost of the purchase you
found in 1st step. Now multiply the interest you found by 30 days, and add it to the total cost of the purchase.
a. $172.56
b. $174.73
c. $190.77
d. $200.26
Answer:
First find the sales tax: $160 \times 0.0785 = $12.56.
Then add the sales tax to the price of the purchase to find the total cost: $160 + $12.56 = $172.56.
Next find the daily interest rate: $0.042\% = 0.00042$.
Then multiply the daily interest rate by the total cost to find the interest per day: $0.00042 \times $172.56 = $0.0725752$.
Finally, multiply the interest per day by 30 days to find the total interest and add it to the total cost to find the final answer: $0.0725752 \times 30 = $2.177256 + $172.56 = $174.737256 \approx $174.74.
So the answer is b.
Is x/5 linear? Please help
Answer:
Yes, x/5 is a linear equation. A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable x is 1, so it is a linear equation.
The graph of x/5 is a straight line with a slope of 1 and a y-intercept of 0.
Mo had 2 goals in one game out of 6 shots attempted, find the experimental probability Mo will shoot a goal when attempted
Answer:
0.0772 OR 0.95 OR 7.72
Step-by-step explanation:
A player makes 622 shots on goal and in that time scores 48 goals.
48 goals ÷ 622 shots = 0.0772.
This player’s shooting percentage is 0.0772, or 7.72%.