If the area of a pad is 17. 5 square yards, the length of the pad is 5 yards, the width of the pad is 3.5 yards.
The formula for the area of a rectangle is:
Area = length x width
We know that the area of the pad is 17.5 square yards, and the length is 5 yards. We can use this information to solve for the width.
Let's substitute the values we know into the formula:
17.5 = 5 x width
To solve for the width, we need to isolate it on one side of the equation. We can do this by dividing both sides by 5:
17.5/5 = width
Simplifying the left side gives:
3.5 = width
In conclusion, Mr. Tomas should make a rectangular concrete pad that is 5 yards long and 3.5 yards wide to have an area of 17.5 square yards.
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Find the missing length A=50 b=50
The value of sides a and b from the triangle. A = 50 degrees, B = 50 degrees, c = 12 meters is 9.341 metres and angle C is 80 dgree.
How can the angles and the sides be determined?From the Law of Sines states that the follow proportions must be true which is
sin (A)/a = sin (B)/b= sin (C)/c
Where A = 50 degrees
B = 50 degrees
c = 12 meters
Angle C = (180-100=80 ( angle in the triangle is 180 degree)
sin (50)/a = sin (50)/b= sin (80)/12
0.766/a = 0.766/b= 0.985/12
0.766/a = 0.766/b=0.082
0.766/a =0.082
a =0.766/0.082 = 9.341
0.766/b=0.082
b=0.766/0.082= 9.341
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complete questions
Solve the given triangle. A = 50 degrees, B = 50 degrees, c = 12 meters
Round your answers to the nearest integer.
C = ? degrees
b = ? meters
c = ? meters
what is the surface area of prism. base=5. height=2. length=3
Answer:
62
Step-by-step explanation:
Surface area of a prism = S = 2(lw + lh + wh)
where l = length
w = width
h = height
Given l = 3, w = 5 and h = 2
S = 2(3 x 5 + 3 x 2 + 5 x 2)
= 2(15 + 6 + 10)
= 2(31)
= 62
What function does this graph represent?
We can conclude after answering the provided question that If the data expression points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.
what is expression ?In mathematics, an expression is a grouping of representations, digits, and huge corporations that resemble a clear relationship or regimen. An expression can be a real number, a transitory, or a combination of the two. Addition, subtraction, pervasiveness, division, and exponentiation are examples of mathematical operators. Expressions are common in arithmetic, mathematics, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.
This graph appears to be a scatter plot of data points based on the visual representation you provided. The values of an independent variable are represented by the horizontal axis (x-axis), while the values of a dependent variable are represented by the vertical axis (y-axis).
Without any additional information, determining the specific function represented by this graph is difficult. The shape and pattern of the scatter plot, on the other hand, can provide some insight into the relationship between the two variables. If the data points are arranged in a linear pattern, for example, the function could be a linear equation. If the data points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.
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i. How does a person's cycling rate show up in his or her equation?
A person's cycling rate can be expressed mathematically in the equation that describes their cycling motion. Specifically, the cycling rate can be represented by the frequency or number of revolutions per unit time (usually in seconds) that the person completes while cycling.
The equation that describes a person's cycling motion is typically a kinematic equation that relates the person's position, velocity, and acceleration as a function of time. One commonly used equation is:
d = vit + 1/2at^2
where d is the distance traveled by the person, vi is the initial velocity (usually zero), a is the acceleration, and t is the time elapsed.
The cycling rate can be incorporated into this equation by expressing the velocity as a function of the frequency of revolutions (f) and the radius of the wheel (r). This gives:
v = 2πrf
where v is the velocity of the cyclist, r is the radius of the wheel, and π is the mathematical constant pi (approximately 3.14).
Substituting this expression for v into the kinematic equation gives:
d = (2πrf)t + 1/2at^2
This equation shows how the person's cycling rate, represented by the frequency f, affects their distance traveled as a function of time. If the person increases their cycling rate, their velocity increases, and they will travel a greater distance in the same amount of time.
An account with an initial balance of $3500 earns interest that is compounded annually. If no other deposits or withdrawals are made, the account will have a balance of $4390.40 after 2 years. Find the annual interest rate.
Therefore, the annual interest rate is approximately 12%.
What factors determine interest rates?How to compute interest is as follows: P x R x T is the formula for calculating interest. Principal Amount is P. (the beginning balance). rates of interest (usually per year, expressed as a decimal). T stands for the value T. (generally one-year time periods).
Let r be the annual interest rate as a decimal. Then the balance after 2 years is given by:
Balance = 3500(1+r)²
Setting this equal to $4390.40 and solving for r, we have:
4390.40 = 3500(1+r)²
Dividing both sides by 3500 and taking the square root, we get:
(1+r)² = 4390.40/3500 = 1.2544
Taking the square root of both sides, we get:
1 + r = √(1.2544) ≈ 1.12
Subtracting 1 from both sides, we get:
r ≈ 0.12 or 12%
Therefore, the annual interest rate is approximately 12%.
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find the values of a, b, and c in the equation 5x^2-2=2x^2+10x+6
The value οf a = 3, b=-10, c-8
What is quadratic equatiοn?it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm. A nοn-zerο term (a 0) fοr the cοefficient οf x² is a prerequisite fοr an equatiοn tο be a quadratic equatiοn.
The x² term is written first, then the x term, and finally the cοnstant term is written when cοnstructing a quadratic equatiοn in standard fοrm. In mοst cases, the numerical values οf letters a, b, and c are expressed as integral values rather than fractiοns οr decimals.
The equatiοn given 5x²-2=2x²+10x+6
3x²-10x-8=0
values οf a = 3, b=-10, c-8
Hence the value οf a = 3, b=-10, c=8
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Use the equation y = 7x to complete the table. What are the missing values of
y?
O A. When x = 2, y = 16.
When x = 4, y = 30.
O B. When x = 2, y = 14.
When x = 4, y = 28.
C. When x = 2, y = 8.
When x = 4, y = 22
D. When x = 2, y = 12.
When x = 4, y = 24.
Using the equation y = 7x , we can compute that when x = 2, y = 14 and when x = 4 , y = 28. So, correct option is B.
The equation y = 7x relates the variables y and x, where y is a function of x. To compute the value of y for a given value of x, we simply substitute that value of x into the equation and solve for y.
When x = 2, we can substitute this value into the equation:
y = 7(2) = 14
Therefore, when x = 2, y = 14.
Similarly, when x = 4, we can substitute this value into the equation:
y = 7(4) = 28
Therefore, when x = 4, y = 28.
So, the correct option is B: When x = 2, y = 14 and when x = 4, y = 28.
In summary, to compute the value of y for a given value of x using an equation, we substitute that value of x into the equation and solve for y. In this case, when x = 2, y = 14, and when x = 4, y = 28, according to the given equation y = 7x.
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Equations with x in the denominator
Can someone please explain to me, step by step, how to answer this question.
Answer:
x=5/6
Step-by-step explanation:
lcm=6x
6xX1/2x+6xX1/3x=6xX1 (divide through)
3x1+2x1=6xX1
3+2=6x
5=6x
5/6=6x/6 (divide through)
x=5/6
Hope it help
Solve the equation by factoring:
9y^2 - 49=0
Answer:
Step-by-step explanation:
do it yourself
a) Work out the angle of elevation from R to T in the rectangle below. Give your answer to 1.d.p. b) Which angle fact tells you that the answer to part a) is also the angle of depression from T to R? 340cm 165cm
a) Note that the Angle of Elevation from R to T is 63.4°
b) The angle fact tells you that the answer to part a) is also the angle of depression from T to R is "the Alternate Angle Postulate"
What is the justification for the above response?
The principle used in below is SOH CAH TOA.
a) Tanθ = Opp/Adjacent
Tanθ = 340/165
Tanθ = 2.0606060606
θ = Tan⁻¹ 2.0606060606
θ = 63.4349
θ [tex]\approx[/tex] 63.4
b) The principle of alternate angles is a theorem in geometry that states that when a straight line intersects two other lines, the angles formed on opposite sides of the intersection and on opposite sides of the transversal are equal. This principle is based on the fact that parallel lines cut by a transversal create corresponding angles that are congruent.
Thus the angle fact tells you that the answer to part a) is also the angle of depression from T to R is "the Alternate Angle Postulate"
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Weights of adult males.
The weights of adult individuals in a certain country are normally distributed with a population mean of μ=172 pounds and a population standard deviation of σ=29 pounds. Suppose n=36 individuals are sampled.
1)
What is the mean of the sampling distribution of the means?
The sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.
In the context of sampling distribution of the means, the standard deviation represents the degree of spread or variation of sample means around the true population mean.
To compute the standard deviation of the sampling distribution of the means, one typically divides the population standard deviation by the square root of the sample size.
Therefore, the standard deviation of the sampling distribution of the means is 29/√36 = 29/6 = 4.83 pounds.
So, the sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.
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I need help working this out, I only need help with question a.
Answer:
-3, -1 and 1
Step-by-step explanation:
substitute what ever the x column says into 2x-3
2×0-3=-3
2×1-3=-1
2×2-3=1
the answers: -3, -1, 1
In Cape Town there is a shortage of water and so water is getting more expensive. Water from the tap costs a flat rate of 15 plus per liter. Water from the store costs 3 per liter. At what number of liters would the cost from the store and the cost from the tap be the same ?
The cost of water from the store and the cost from the tap will be the same when the number of liters
reaches 7.5 liters.
Let's assume that the cost of buying 'x' liters of water from the store is the same as the cost of buying 'x' liters of water from the tap.
For water from the store, the cost per liter is 3, so the cost of buying 'x' liters of water from the store would be 3x.
For water from the tap, there is a flat rate of 15 plus per liter. So, the cost of buying 'x' liters of water from the tap would be 15 + x.
Now we can set up an equation to find the value of 'x' when the costs are equal:
3x = 15 + x
Simplifying this equation, we get:
2x = 15
x = 7.5
Therefore, the cost from the store and the cost from the tap would be the same at 7.5 liters.
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How many terms are in the expression: 12p + 8m + 2
Answer: I THINK 4.
Step-by-step explanation:
Sorry if it is wrong!! :'D
2.4 m × 0.7 m Find the length volume = 1.512 meters³
The length of the rectangular prism with a volume of 1.512 m³ is equal to 0.9 meters.
How to calculate the volume of a rectangular prism?Mathematically, the volume of a rectangular prism can be calculated by using this formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given parameters into the formula for the volume of a rectangular prism, we have;
Volume of a rectangular prism = L × W × H
1.512 = L × 2.4 × 0.7
Length, L = 1.512/1.68
Length, L = 0.9 meters.
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Complete Question:
Find the length of the rectangular prism shown below with a volume of 1.512 m³, a width of 2.4 m and a height of 0.7 m.
I choose 10 consecutive numbers. if I exclude one of the numbers the remaining 9 sum to 2023 which number did I exclude?
Answer:
the number 228
Step-by-step explanation:
Let's call the smallest number in the consecutive sequence "x". Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.
If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:
(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) or 9x + 36.
We know that the sum of the remaining 9 numbers is 2023, so we can set up the equation:
9x + 36 = 2023
Solving for x, we get:
9x = 1987
x = 221
Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.
If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.
a fair ordinary dice is thrown once
select the probability a 4 or a 5
A/1/6 B/2/6 C 4/6 D/5/6
Find the missing length of the triangle. 7.2 feet, 9.6 feet, and c
By using pythagorean theorem, the length of the missing side is 12 feet.
What is the Pythagorean theorem?
Pythagoras' theorem is a fundamental principle in geometry that relates to the three sides of a right-angled triangle. It states that:
"In a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides."
In mathematical terms, if a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse, then the theorem can be written as:
[tex]c^2 = a^2 + b^2[/tex]
We can use the Pythagorean theorem to determine the length of the missing side if we know that the given sides form a right triangle.
In this case, we have two sides of the triangle given: 7.2 feet and 9.6 feet. Let's assume that c is the length of the hypotenuse.
If the triangle is a right triangle, then we can use the Pythagorean theorem to solve for c:
[tex]c^2 = 7.2^2 + 9.6^2[/tex]
[tex]c^2 = 51.84 + 92.16[/tex]
[tex]c^2 = 144[/tex]
[tex]c = \sqrt{144}[/tex]
c = 12 feet
Therefore, if the triangle is a right triangle, then the length of the missing side is 12 feet.
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HELPPPPPPPPPPPPpppppppppppppppppppppppp
Answer:C
Step-by-step explanation:
[tex](x-3)^2=5\\we \ should \ find \ square \ root \ of \ each \ side,\\\sqrt{(x-3)^2}=\sqrt{5}\\1)x-3=\sqrt{5}x=\sqrt{5}+3\\2)3-x=\sqrt{5}\\x=3-\sqrt{5}\\\\so,x=3\± \sqrt{5}[/tex]
Seven liters of cran-strawberry juice is added to an unknown amount of cran-orange juice to make a fruit punch. The cran-strawberry juice contains 65% cranberry juice. The cran-orange juice contains 50% cranberry juice. The fruit punch contains 60% cranberry juice. How much cran-orange juice does the fruit punch contain?
50%
The cran-orange juice contains 50% cranberry juice. The juice is 100% juice. Subtract 50% cranberry juice from 100% cran-orange juice and that leaves you with 50% orange juice.
Baxter’s Hardware has some followers on their social media account on Friday. On Saturday, the account gains 18 new followers. On Sunday, 20 people stop following the Baxter’s Hardware account. Baxter’s Hardware has 25 followers on Monday morning. The equation f + 18 - 20 = 25 represents the situation. Solve the equation. Be sure to show your work.
Please answer quick!!!
According to given equation Baxter’s Hardware had 27 followers on Sunday morning.
What is equation?
Equations can take many forms, including linear, quadratic, polynomial, trigonometric, and exponential, and can be used to model and solve a wide range of real-world problems.
The given equation is:
f + 18 - 20 = 25
Adding the numbers on the left side, we get:
f - 2 = 25
Adding 2 to both sides, we get:
f - 2 + 2 = 25 + 2
Simplifying, we get:
f = 27
Therefore, Baxter’s Hardware had 27 followers on Sunday morning.
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If a1=5 and an=an-1-4 then find the value of a5
A5 has a value of -11. This can also be confirmed by looking at the words in order: 5, 1, -3, -7, and -11.
Using the given formula, we can find the value of the nth term by recursively applying the formula, starting from the first term:
a1 = 5
a2 = a1 - 4 = 1
a3 = a2 - 4 = -3
a4 = a3 - 4 = -7
a5 = a4 - 4 = -11
Therefore, the value of a5 is -11. We can also verify this by checking the sequence of terms: 5, 1, -3, -7, -11.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
The answer is B
Step-by-step explanation:
URGENTTTTT!!!!!!!!!! please complete the chart with the correct angle measures
(numbers 6-9 please!)
Answer:
9 hope u get it right budddyyyy
what is the value of the expression
3/5(X-8)-y
when x=15 and y=1/10
a 11/10
b 21/10
c 31/10
d 41/10
Answer:
The answer is to this question is D. 41/10
The pH of a solution is given by the formula pH=−logH+, where H+ is the concentration of hydrogen ions in moles per liter in the solution. Lye has a pH of 12.13. Use this formula to find the hydrogen ion concentration, [H+]. Round to one decimal place if necessary.
Given data:
pH of lye = 12.13
Using the formula pH = -log[H+], we have to find the hydrogen ion concentration, [H+].
Now, putting the given values in the formula, we get:
pH = -log[H+]
12.13 = -log[H+]
log[H+] = -12.13
[H+] = 10^-12.13 = 5.01187 x 10^-13
So, the hydrogen ion concentration, [H+] is 5.01187 x 10^-13 moles/liter. Therefore, the answer is 5.01187 x 10^-13.
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the height of a cylindrical pole is 12 feet and its circumference is 2 feet. a rope is attached to a point on the circumference at the bottom of the pole. the rope is then wrapped tightly around the pole four times before it reaches a point on the top directly above the starting point at the bottom. what is the minimum number of feet in the length of the rope? express your answer in simplest radical form.
The minimum number of feet in the length of the rope [tex]8\sqrt{(4\pi^2 + 36)}[/tex] feet.
To find the minimum number of feet in the length of the rope, we need to first calculate the height of the point on the circumference where the rope is attached. We can do this by using the formula for the circumference of a cylinder:
C = 2πr
where C is the circumference, r is the radius of the cylinder, and π is pi. Since we know that the circumference of the pole is 2 feet, we can solve for the radius:
2 = 2πr
r = 1/π
Next, we need to calculate the length of the rope that is wrapped around the pole. We know that the rope is wrapped around the pole four times, so the length of the rope is:
L = 4 × height of the pole
To find the height of the pole, we can use the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
where a is the radius of the pole, b is the height of the point where the rope is attached, and c is the length of the rope wrapped around the pole.
Solving for b, we get:
b = [tex]\sqrt{c^2 - a^2)}[/tex]
Substituting the values we know, we get:
b = [tex]\sqrt{((4\pi^2 + 12^2) - \pi^2)}[/tex]
b = [tex]\sqrt{sqrt(16\pi^2 + 144)}[/tex]
Finally, we can substitute this value into the formula for the length of the rope:
[tex]L = 4 * \sqrt{16\pi^2 + 144)}[/tex]
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the basis for using a normal probability distribution to approximate the sampling distribution of the sample means and population mean is . a. the empirical rule b. chebyshev's theorem c. bayes' theorem d. the central limit theorem
The cοrrect answer tο the given questiοn is d. the central limit theοrem.
What is frequency distributiοn?The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.
The basis fοr using a nοrmal prοbability distributiοn tο apprοximate the sampling distributiοn οf the sample means and pοpulatiοn mean is the central limit theοrem.
The central limit theοrem states that fοr a sufficiently large sample size, the sampling distributiοn οf the sample means will be apprοximately nοrmal, regardless οf the shape οf the pοpulatiοn distributiοn. This theοrem allοws us tο make statistical inferences abοut the pοpulatiοn mean based οn the sample mean using the prοperties οf the nοrmal distributiοn, such as the mean and standard deviatiοn.
Therefοre, the cοrrect answer tο the given questiοn is d. the central limit theοrem.
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Using Unit Rates to compare Ratios continued
5 Branden and Pete each play running back. Branden carries the ball 75 times for
550 yards, and Pete has 42 carries for 380 yards. Who runs farther per carry?
Pete did more his outcome was 9. 0 which was bigger the branden do
380 divided by 42 for your answer
Pete runs farther per carry, with a unit rate of 9.05 yards per carry compared to Branden's unit rate of 7.33 yards per carry.
A unit rate is a rate that has a denominator of 1. It is a ratio that compares a quantity to its unit of measurement.
To determine who runs farther per carry, we can use unit rates to compare the distance each player runs per carry.
For Branden:
Distance per carry is
= 550 yards ÷ 75 carries
Divide the numbers
= 7.33 yards per carry
For Pete:
Distance per carry is
= 380 yards ÷ 42 carries
Divide the numbers
= 9.05 yards per carry
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Let X be a normally distributed random variable. Given that the
mean is 2 and P(X < 2.24) = 0.7257, what is the variance?
a. 0.5266
b. None of the suggested answers are correct
c. 0.6
d. 0.4
e. 0.1
e [0.1}
We know that P(X < 2.24) = 0.7257. Also, the mean is 2.Let us calculate the variance of the given normal distribution random variable. Given that P(X < 2.24) = 0.7257, we have to find variance. Let us solve this question as follows:We know that mean of normally distributed random variable is μ and standard deviation is σ. As the mean is 2, μ = 2.We have the z-score: z = (2.24 - 2) / σFrom the normal distribution table, we can find out that P(Z < 0.80) = 0.7881Now, we have the following equation:0.7881 = (2.24 - 2) / σσ = 0.3158Finally, we can find the variance (σ^2) = 0.3158^2 = 0.0995 ≈ 0.1Therefore, the correct answer is option e. 0.1.
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