The lengths of the legs of a right triangle are 3 cm and 4 cm. What is the length of the hypotenuse?
To find the length of the hypotenuse of a right triangle with legs measuring 3 cm and 4 cm, use the Pythagorean theorem formula c = √(a² + b²). Plugging in the values gives c = √(9 + 16), which results in a hypotenuse of 5 cm.
The student is asking how to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are given. In this case, the legs of the triangle are 3 cm and 4 cm long. To find the hypotenuse, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be expressed as a formula: a² + b² = c². Solving for c, we can find the hypotenuse by taking the square root of the sum of the squares of the other two sides:
c = √(a² + b²)
Plugging in the values for a and b:
c = √(3 cm)² + (4 cm)²
c = √(9 cm² + 16 cm²)
c = √25 cm²
c = 5 cm
Therefore, the length of the hypotenuse is 5 cm.
There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 252.5 grams of this cereal.
Given:
Amount of calories per 117.4 grams of Cereal X
= 110 or 0.620068 per 1 gram of cereal X
Solution:
If there are 252.5 grams of cereal X then the amount of calories in it is computed as
0.620068 X 252.5
156.5671 or 157 (rounded off)
Please help with answering this problem.
suppose each bag costs $14.99. estimate the total cost of 5 bags
what inequality represents "a cat weighs no more than 8 pounds"
Final answer:
The inequality representing "a cat weighs no more than 8 pounds" is expressed as w ≤ 8, where w symbolizes the cat's weight in pounds. This concept illustrates how inequality symbols are applied in algebra to represent the relationship between quantities, applicable in various real-world scenarios.
Explanation:
The question asks which inequality represents "a cat weighs no more than 8 pounds." In mathematical terms, this statement can be translated using an inequality symbol that indicates the cat's weight is either equal to or less than 8 pounds. The appropriate symbol for this is “≤”, which stands for “less than or equal to.” Therefore, the inequality that represents this statement is w ≤ 8, where w represents the weight of the cat in pounds.
Using inequality symbols to show how two metric measurements are related is a foundational concept in algebra, and it is crucial when working with real-world scenarios where quantities have upper or lower bounds. For instance, understanding this concept can apply to various situations such as determining the weight of a dog, or comparing soda in a can to ensure it does not exceed a certain weight limit. It's important to grasp how these symbols convey relationships between quantities.
Select from the drop-down menu to correctly identify the property shown.
(−5.2+ (−8.4)) + (−2.8) = −(5.2 + 8.4) + (−2.8)
Associative property
Commutative property
Opposite of sum property
Factor 2x2 - 9x - 11.
x2 + y2 – 10x + 6y = 15.
Loretta deposited $429 in a new savings account at Henry County Bank and Trust. She made no other deposits or withdrawals. After 6 months, the interest was computed at an annual rate of 6 .25%. How much simple interest did her money earn?
There are two major tests of readiness for college, the act and the sat. act scores are reported on a scale from 1 to 36. the distribution of act scores are approximately normal with mean μ = 21.5 and standard deviation σ = 5.4. sat scores are reported on a scale from 600 to 2400. the sat scores are approximately normal with mean μ = 1498 and standard deviation σ = 316. alyssa scores 30 on the act. assuming that both tests measure the same thing, what score on the sat is equivalent to alyssa's act score? (round your answer to a whole number.)
Assuming that both tests measure the same thing, the equivalent sat score is 1994
The given parameters are:
ACT scores
Mean, μ = 21.5
Standard deviation, σ = 5.4
Score, x = 30
SAT scores
Mean, μ = 1498
Standard deviation, σ = 316
Start by calculating the z-score for the act score using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{30 - 21.5}{5.4}[/tex]
[tex]z = 1.57[/tex]
Next, calculate the z-score for the sat score using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{x - 1498}{316}[/tex]
Substitute 1.57 for z
[tex]1.57 =\frac{x - 1498}{316}[/tex]
Multiply both sides by 316
[tex]496.12 =x - 1498[/tex]
Solve for x
[tex]x = 496.12 + 1498[/tex]
[tex]x = 1994.12[/tex]
Approximate
[tex]x = 1994[/tex]
Hence, the equivalent sat score is 1994
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Final answer:
The equivalent SAT score to Alyssa's ACT score of 30 is calculated using Z-scores. The result is an SAT score of approximately 1996, rounded to the nearest whole number.
Explanation:
To determine what SAT score is equivalent to Alyssa's ACT score of 30, we use the concept of Z-scores. A Z-score represents the number of standard deviations an observation is from the mean of a distribution. The formula for calculating a Z-score is given by Z = (x - μ) / σ, where x is the score of interest, μ is the mean, and σ is the standard deviation.
First, we calculate the Z-score for Alyssa's ACT score:
ACT mean (μ) = 21.5
ACT standard deviation (σ) = 5.4
Alyssa's ACT score (x) = 30
Z-score for ACT = (30 - 21.5) / 5.4 ≈ 1.5741
Now we use Alyssa's ACT Z-score to find the equivalent SAT score by applying it to the SAT distribution. The SAT mean (μ) is 1498 and the SAT standard deviation (σ) is 316.Equivalent SAT score = SAT mean + (Z-score × SAT standard deviation)
Equivalent SAT score = 1498 + (1.5741 × 316) ≈ 1996
Therefore, rounding to the nearest whole number, the SAT score equivalent to Alyssa's ACT score of 30 is 1996.
3x3 systems answers 4x + 8y + z = 2 x + 7y - 3z = -14 2x - 3y + 2z = 3
The cost of producing x pumpkin pies at a small bakery is given by c(x)=49+1.75x. Find the cost of producing 25 pies A. $74.00 B.$81.50 C.$92.75 D.$108.25
A function is defined as a relation between a set of inputs having one output each.
Input = 25 and output = $92.75
The cost of 25 pies is $92.75
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
Example: f(x) = 2 + 3x
x = 1
f(1) = 2 + 3x1 = 2 + 3 = 5
1 = Domain
5 = Range
We have,
c(x) = 49 + 1.75x
x = number of pies
The cost of producing 25 pies:
c(25) = 49 + 1.75 x 25
= 49 + 43.75
= $92.75
Thus the cost of 25 pies is $92.75
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what is the value of 6 in 89.6
Sara can type 90 words in 4 minutes about how many words would you expect her to type in 10 minutes at this rate
Answer:
C. 225 words
Step-by-step explanation:
90 / 4 = 22.5
22.5 x 10 = 225 words
A) if f(x) = 6x/(2 + x2), find f '(2) and use it to find an equation of the tangent line to the curve y = 6x/(2 + x2) at the point (2, 2). f '(2) = incorrect: your answer is incorrect. y(x) =
The equation of the tangent line to the curve y = 6x/(2 + x²) at the point (2, 2) will be y-2=(1/3)x-2.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that,
f(x) = 6x/(2 + x²)
f'(x)=(6x)(2+x²)-6x(2+x²)/(2+x²)²
f'(2)=(6×2)(2+2²)-6x(2+2²)/(2+2²)²
f'(2)=1/3
The value of functions gives the slope of the equation passes through the point (2, 2).
y-y₀=m(x-x₀)
y-2=(1/3)x-2
Thus, the equation of the tangent line to the curve y = 6x/(2 + x²) at the point (2, 2) will be y-2=(1/3)x-2.
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Use cylindrical coordinates to evaluate the integral where d is the solid bounded above by the plane z=2 and below by the surface 2z=x2+y2
Answer:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \frac{32 \pi}{5}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Multivariable Calculus
Cylindrical Coordinate Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]Volume Formula [Cylindrical Coordinates]:
[tex]\displaystyle V = \iiint_T \, dV \rightarrow V = \iiint_T {r} \, dz \, dr \, d\theta[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \text{Region} \ D \left \{ {{2z = x^2 + y^2} \atop {z = 2}} \right.[/tex]
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz[/tex]
Step 2: Find Volume Pt. 1
Find θ bound.
[Surface] Substitute in plane z:Find r bound.
[Surface] Substitute in plane z:Find z bound.
[Surface] Substitute in cylindrical conversions:Step 3: Find Volume Pt. 2
[Integrals] Substitute in cylindrical conversions:∴ the integral bound by region D is equal to [tex]\displaystyle \bold{\frac{32 \pi}{5}}[/tex].
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Topic: Multivariable Calculus
Unit: Triple Integrals Applications
Identify the phrase that cannot be described by the same absolute value as the other three. Explain your reasoning.
What is 3.313 Rounded to the nearest tenth
sin pi/4 sin pi/6= 1/2(_____ pi/12-cos 5pi/12)
Answer:
[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]
Step-by-step explanation:
We are given that
[tex] sin\frac{\pi}{4} sin\frac{\pi}{6}[/tex]
We have to correct value in blank space.
We know that identity
[tex] sin xsiny=\frac{cos(x-y)-cos(x+y)}{2}[/tex]
Using this identity
[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{\pi}{4}-\frac{\pi}{6})-cos(\frac{\pi}{4}+\frac{\pi}{6})}{2}[/tex]
[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{3\pi-2\pi}{12}-cos(\frac{3\pi+2\pi}{12})}{2}[/tex]
[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]
Answer:[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]
Andrew make six dollars an hour +9 dollars an hour for every hour of overtime overtime hours are any hours more than 40 hours for the week. Create an equation that shows the amount of wages earned S for working why hours of overtime. Can’t remember to include in the equation the amount earned from working 40 hours
what symbol makes the statement true 307 324
addition or subtraction of unit fractions 1/2-1/8=
A customer pays $1,100 in state taxes on a newly purchased car. What is the value of the car if state taxes are 8.9% of the value?
$9,765.45
$10,876.90
$12,359.55
$14,345.48
$15,745.45
Final answer:
To find the value of the car, divide the amount of state taxes paid by the tax rate percentage. The value of the car is $12,359.55.
Explanation:
To find the value of the car, we need to divide the amount of state taxes paid by the tax rate percentage. In this case, the state taxes paid is $1,100 and the tax rate is 8.9%.
So, the value of the car can be calculated as follows:
Value of the car = State taxes paid / Tax rate percentage
= $1,100 / 0.089
= $12,359.55
Therefore, the value of the car is $12,359.55
Please help???
Which of the following equations represents the graph shown?
A) f(x)=-x+2
B) f(x)=-x-2
C) f(x)=x+2
Okay it's not C, it's wrong
Answer:
the answer is f(x) = -x + 2
Step-by-step explanation:
because i got it right
gary father dropped him off soccer practice at2:45 pm .his mom picked him up at 5:00 pm.how long did soccer practice last
Express ratio in simplest form 18 feet : 5 yards
Final answer:
To simplify the ratio 18 feet to 5 yards, convert yards to feet to get 15 feet, then divide both by the greatest common divisor, 3, ending up with a simplified ratio of 6:5.
Explanation:
To express the ratio 18 feet: 5 yards in simplest form, we first need to convert either yards to feet or feet to yards so that we are comparing the same units. Since we know that 1 yard is equal to 3 feet, we can multiply the number of yards by 3 to find out how many feet it equates to.
Now, let's calculate:
5 yards × 3 feet/yard = 15 feet
So the ratio 18 feet: 5 yards can be rewritten as 18 feet: 15 feet. To simplify this ratio, we divide both numbers by their greatest common divisor (GCD), which in this case is 3.
Here is the calculation:
18 feet ÷ 3 = 6
15 feet ÷ 3 = 5
Therefore, the ratio in simplest form is 6: 5.
5 hundreds 6 ten thousands 2 ones
Describe when you would need to solve a system of linear equations, instead of a single linear equation. (Site 1)
a single linear equation: you sell a budweiser for $3 a bottle & make $42.
a device: you promote budweiser for $3 and heineken for $4.
the entire wide variety of beers you promote is 10 and you make total of $forty.
what's linear equation components?The slope-intercept form of a linear equation is y = mx + b. in the equation, x and y are the variables. The numbers m and b deliver the slope of the line (m) and the fee of y when x is zero (b). The value of y whilst x is zero is known as the y-ithat ntercept due to the fact (zero,y) is the factor at which the road crosses the y-axis.
How do I solve linear equations?clean fractions or decimals.Simplify each aspect of the equation via doing away with parentheses and mixing phrases.Isolate the variable term on one side of the equation.remedy the equation by means of dividing each aspect of the equation.take a look at your solution.Learn more about linear equations here: https://brainly.com/question/1884491
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Tasha earns $400 per week plus a commission of 10% on her weekly sales. Each week she saves of her earnings. In the expression , what does the expression 400 + 0.1s represent in this situation?
PLEASE HELP ME!?!?
A square pyramid was sliced perpendicular to its base but not through its vertex. What is the shape of the cross section shown in the figure?
A.) a parallelogram that is not a rectangle or a square
B.) a rectangle that is not a square
C.) a square
D.) a trapezoid
The shape of the cross-section for a square pyramid sliced perpendicular to its base but not through its vertex is a trapezoid.
What is a pyramid?A pyramid is a three dimensional shape (have length, width and height) with a polygon face and lateral faces which are triangular.
A square pyramid have a square base and triangular lateral faces.
The shape of the cross-section for a square pyramid sliced perpendicular to its base but not through its vertex is a trapezoid.
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Answer:
should be a trapezoid, in other words, its D
Step-by-step explanation: