The best height he can jump is 2.5 meters. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
It is believed that the four fundamental operations, often known as "arithmetic operations," adequately explain all real numbers. Division, multiplication, addition, and subtraction are the mathematical operations that come before quotient, product, sum, and difference.
We are given that Ivan Ukhov jumps 2.4 metres which is 4% lower than the best height he can jump.
Let the best height be 'x'.
So, from the above information, we get
⇒ x - 0.04x = 2.4
⇒ 0.96x = 2.4 (Using subtraction)
⇒ x = 2.5 (Using division)
Hence, the best height he can jump is 2.5 meters.
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determine whether Rolle’s Theorem can be
applied to on the closed interval If Rolle’s Theorem can
be applied, find all values of in the open interval such
that If Rolle’s Theorem cannot be applied, explain
why not
Rolle’s Theorem can be applied to the closed interval.
What is the Rolle’s Theorem?
In essence, Rolle's theorem or Rolle's lemma argues that there must be at least one stationary point—a position where the first derivative is zero—between any two separate sites where a real-valued differentiable function achieves equal values. The theorem bears Michel Rolle's name.
Here, we have
Given: f(x) = -x² + 3x, [0,3]
We must determine whether Rolle’s Theorem can be applied to the closed interval.
f(x) is continuous in the closed interval [0,3].
f(x) is differentiable in the open interval (0,3)
f(0) = 0 + 0 = 0
Rolle's theorem can be applied.
f'(x) = -2x + 3
f'(x) = 0
-2x + 3 = 0
3 = 2x
x = 2/3
2/3 lies inside the [0,3].
Hence, Rolle’s Theorem can be applied to the closed interval.
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Bridget is a salesperson. She sold a television for $320 and earned a 5% commission. How much commission did Bridget earn?
In this case, Bridget's commission rate is 5%, which can also be written as [tex]0.05[/tex] (since 5% is equivalent to 5/100 or 0.05 as a decimal). Bridget earned a commission of $ [tex]16[/tex] on the sale of the television.
What commission did Bridget earn?To calculate the commission that Bridget earned, we can use the formula:
commission [tex]= (percentage/100) \times sale price[/tex]
where the sale price is the price of the television that Bridget sold, and the percentage is the commission rate, which is 5%.
Using this formula, we can calculate the commission as:
commission[tex]= (5/100) \times $320 = $16[/tex]
Therefore, Bridget earned a commission of $ [tex]16[/tex] on the sale of the television.
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[Maximum mark: 5] The diagram shows a sector AOB of a circle with centre O and radius r. The triangle AOB is equilateral and has perpendicular height 5 cm.
a) show that the radius of the sector is 10√3/3 cm.
b) find in terms of π, the perimeter P of the sector.
Answer:
Step-by-step explanation:
In (b) you may be more used to the formula for arc length: [tex]P=\frac{\theta }{180} \times \pi r[/tex].
The result is the same.
Can anyone help me answer this? the question is given below?
For the second attachment was the question
The average rate of change of the function is 3.
How to find the average rate of change of a function?The average rate of change of a function is given by the formula:
average of change = (f(b) - f(a)) / (b - a)
Where [a, b] is the interval of the function
f(x) = x³ + 2x; [-1, 1]
average rate of change = ([ 1³ + 2(1)] - [ (-1)³ + 2(-1)]) / (1 - (-1))
average rate of change = (3 - (-3))/(1 + 1)
average rate of change = 6/2
average rate of change = 3
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A wire that is centimeters long is shown below.
The wire is cut into two pieces, and each piece is bent and formed into the shape of a square.
Using properties of square,
a. Equation for total area = 2x² - 16x + 64
b. Area will be minimum for the value of x = 0
c. Minimum area will be 64cm².
Define a square?With four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. The equal sides and 90° internal angles of each square form serve as indicators of its identity.
Total length of wire = 32cm.
Now side of one square is given as x.
Perimeter of big square will be = 4x.
Now perimeter of small square = 32- 4x.
Side of small square = (32-4x)/4
= 4(8-x)/4
= 8-x
Area of big square = x × x
= x².
Area of small square = (8-x) ².
Now Total area, A(x) = x² + (8-x) ²
= x² + 64 + x² - 16x
= 2x² - 16x + 64
The side length that will minimize the area will be, x = 0.
Minimum area of the total figure will be = 64cm²
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Use an identity to write the expression as a single trigonometric function or as a single number. sin 28⁰/ 1 + cos 28°
Answer: We can simplify the expression by using the identity for the tangent of half an angle:
tan(x/2) = sin(x) / (1 + cos(x))
where x is the angle in radians. We can use this identity by setting x = 56° since 2*28°= 56°.
So, we have:
sin(28°) / (1 + cos(28°)) = tan(56°/2)
We know that 56°/2 = 28°, so we have:
tan(28°)
Therefore, the expression simplifies to a single trigonometric function:
tan(28°)
Step-by-step explanation:
help pleaseeee
question
What are reasonable constraints for the context?
A) 0 <= x <= 9 and 16 <= y <= 40
2)- 9 <= x <= 9 and - 1.798 <= y <= 17.798;
C) 0 <= x <= 12 and 16 <= y <= 48
D)0 < x < 12 and 16 < y < 48
Option C) 0 <= x <= 12 and 16 <= y <= 48 would be reasonable constraints for the context.
What is the inequality equation?
An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
The x-axis represents the number of hours since 9 AM, which can range from 0 to 12 since the shift ends at 9 PM.
The y-axis represents the number of patients, which can realistically range from 16 to 48 as hospitals can have varying levels of patient traffic.
The constraint includes the endpoints of the range, which makes it more accurate.
Hence, Option C) 0 <= x <= 12 and 16 <= y <= 48 would be reasonable constraints for the context.
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Ruth has $4,942 in an account that earns 12% interest compounded annually.
To the nearest cent, how much will she have in 1 year?
Ruth will have the principal is approximately $5,534.04 in 1 year at earns 12% interest compounded annually.
What is principal?
To find how much Ruth will have in 1 year, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{n*t}[/tex]
where A is the amount after t years, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
Plugging in the given values, we get:
A = [tex]$4,942(1 + 0.12/1)^{1*1}[/tex]
A = $4,942(1.12)
A = $5,534.04
Therefore, Ruth will have approximately $5,534.04 in 1 year.
What is an interest?
Interest is the amount of money charged by a lender to a borrower for the use of money over a period of time. It is typically calculated as a percentage of the amount borrowed or invested, and is often expressed as an annual percentage rate (APR). Interest can be simple or compound, depending on whether it is calculated only on the principal amount or on both the principal and accumulated interest. Interest is an important concept in finance and economics, and is used in a wide range of financial transactions, including loans, investments, and savings accounts.
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Which quadrilateral has one, and only one, line of symmetry?
rectangle square isosceles trapezoid or parallelogram?
Rick has been collecting stamps. After one week, he had collected 6 stamps and each week following, he collected 3 more.
How many stamps will he have after 10 weeks?
[tex]Step-by-step-explanation-& Answer[/tex]
Well if our friend Rick continues the pattern that is shown in the question then the answer is at the bottom
Lets do some addition:
(6+3) * 5 ( 5 x 2 = 10 )
First find the parenthesis, 6 + 3 = 9
Next multiply, 9 x 5 = 45
Thus the answer to your problem is:
[tex]\left[\begin{array}{ccc}A&N&S\\=&=&=\\4&5&!\end{array}\right][/tex]
How long does it take the ball to reach maximum height?
Answer: 1second
Step-by-step explanation:
Jose bought 100 shares of stock at 17 5/8 and sold it for 21 1/4. What was his profit in dollars
Answer: 3.625 or 3 5/8
Step-by-step explanation:
So I personally would turn everything into decimals and subtract.
21.250 -17.625
And using our handy calculator, you get
3.625
IFA has made a football of diameter 14 cm from leather. 3% leather is wasted. If the cost of leather including labo er sq.cm, find the total cost of leather purchased to make
the total cost of leather purchased to make the football is $30.79.
how to find volume of football?The volume of a football can be calculated using the formula for the volume of a sphere:
V = (4/3)πr³
Where r is the radius
Given that the diameter of the football is 14 cm and the radius is half of the diameter, so radius is 7 cm.
So, the volume of the football is:
V = (4/3)π(7 cm)³
= 1437.33 cm³
Now, we know that 3% of the leather is wasted,
so the amount of leather to make the football is:
(100% - 3%) = 97% of the total leather purchased.
Therefore, the amount of leather used to make the football is:
0.97 × 1437.33 cm³ = 1394.19 cm³
To find the total cost of the leather purchased, we need to know the cost of leather per square centimeter. Let's assume that the cost of leather including labor is $0.05 per square centimeter.
The surface area of a sphere can be calculated using the formula:
A = 4πr²
So, the surface area of the football is:
A = 4π(7 cm)²
= 615.75 cm²
the total cost of the leather:
Cost of leather = Cost per square centimeter × Surface area of the football
= $0.05/cm² × 615.75 cm²
= $30.79
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Emma substitutes 3 for x in a one-variable linear equation and finds that it makes the equation true. She then substitutes 5 for x in the same linear equation and finds that 5 also makes the equation true. What can you conclude about the number of solutions of the equation? Explain your reasoning.
The linear equatiοn has infinite sοlutiοns.
What is equatiοn?When twο expressiοns are jοined by the equal sign ('='), a mathematical statement is created. In οrder tο be determined, there must be at least οne unknοwn variable. An equatiοn is sοmething like 3x - 8 = 16. This equatiοn can be sοlved tο yield x = 8.Any οne variable linear equatiοns can have zerο, οne οr infinite sοlutiοns.
Emma substitutes 3 fοr x in a οne-variable linear equatiοn and finds that it makes the equatiοn true. She then substitutes 5 fοr x in the same linear equatiοn and finds that 5 alsο makes the equatiοn true.
If Emma tested twο values 3 and 5 fοr the same οne variable linear equatiοn and they were bοth true sοlutiοns, this means that the equatiοn has mοre than οne sοlutiοn.
If a οne variable linear equatiοn has mοre than οne sοlutiοn, than the equatiοn has infinite sοlutiοns.
Hence, the linear equatiοn Emma is talking abοut has infinite number οf sοlutiοns.
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A point in the table for the transformed function is
Answer:
linear function
Step-by-step explanation:
straight line then add up
Consider the set K = (triangle upsidedown triangle square rectangle)
Let inversion be defined on K as a physical act of turning a member of K upside down. What is triangle?
If inversion be defined on K as a physical act of turning a member of K upside down. Then it will be the upside-down triangle.
consider the set K = (triangle, upside-down triangle, square, rectangle). Inversion is defined on K as the act of turning a member of K upside down.
To determine which shape is the triangle, follow these steps:
1. Identify the properties of each shape in set K:
- Triangle: 3 sides and 3 angles
- Upside-down triangle: same properties as a triangle, but inverted
- Square: 4 sides, all equal in length, and 4 right angles
- Rectangle: 4 sides, opposite sides equal in length, and 4 right angles
2. Analyze the effect of inversion on each shape:
- Triangle: Inverting a triangle results in an upside-down triangle.
- Upside-down triangle: Inverting an upside-down triangle results in a regular triangle.
- Square: Inverting a square does not change its appearance.
- Rectangle: Inverting a rectangle does not change its appearance.
3. Identify the shape that becomes a triangle after inversion:
- The upside-down triangle becomes a regular triangle after inversion.
So, the shape in set K that corresponds to the triangle after applying inversion is the upside-down triangle.
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A group of people were asked if they had run a red light in the last year. 220 responded "yes", and 209 responded "no".
Answer:
[tex]\frac{20}{19}[/tex] or ≈ 1.053
Step-by-step explanation:
We Know
220 responded 'yes', and 209 responded 'no'
Find the probability that if a person is chosen at random, they had run a red light in the last year.
The probability is: [tex]\frac{220}{209}[/tex] = [tex]\frac{20}{19}[/tex] ≈ 1.053
So, the answer is [tex]\frac{20}{19}[/tex] or ≈ 1.053
Find x round to the nearest 100th
Type your response in the box.
Think about the impact on the consumer as you read these scenarios. Then answer the question that follows.
Scenario 1
Carlos is doing his weekly grocery shopping and needs to buy cereal. He turns his cart into the cereal aisle at the store. He sees many different cereals within his price range but notices that some are priced higher than others. He chooses a cereal he recognizes from a TV commercial, even though it’s slightly more expensive than he expected.
Scenario 2
Evelyn wants to purchase a plane ticket to visit her sister in London. She’s been checking prices frequently the past few days and notices that prices aren’t falling as she anticipated. She also notices that despite five airlines flying to London from the city she lives in, the prices of the tickets are all the same. She eventually decides not to go because the prices are too high for her budget.
What affected the purchasing decisions in these two scenarios?
The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.
What is meant by budget?
In general, a budget is a financial plan or estimate that outlines the expected income and expenses over a specific period.
The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.
In scenario 1, Carlos chose a more expensive cereal because he recognized it from a TV commercial, which may have influenced his perception of its quality or desirability.
In scenario 2, Evelyn decided not to purchase a plane ticket because the prices were too high for her budget, despite there being multiple airlines offering flights to London.
Therefore,The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.
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Triangle ABC is reflected over the line y=2 to obtain triangle A'B'C'. Then triangle A'B'C' is translated by the directed line segment from (0,0) to (3,2) to obtain triangle A"B"C".
Answer: To obtain triangle A'B'C' from triangle ABC by reflection over the line y = 2, we reflect each point of the triangle over the line. This gives us:
A' = (A_x, 4 - A_y)
B' = (B_x, 4 - B_y)
C' = (C_x, 4 - C_y)
To obtain triangle A"B"C" from triangle A'B'C' by translation by the directed line segment from (0,0) to (3,2), we add the vector (3,2) to each point of the triangle. This gives us:
A" = (A'_x + 3, A'_y + 2) = (A_x + 3, 6 - A_y)
B" = (B'_x + 3, B'_y + 2) = (B_x + 3, 6 - B_y)
C" = (C'_x + 3, C'_y + 2) = (C_x + 3, 6 - C_y)
Therefore, the vertices of triangle A"B"C" are (A_x + 3, 6 - A_y), (B_x + 3, 6 - B_y), and (C_x + 3, 6 - C_y).
Step-by-step explanation:
In a parallelogram, the longer side is 20 cm longer than twice the shorter side. the perimeter is 130 cm. Find the dimensions (length and width) of the parallelogram. Whats the answer and solution?
Answer:
15 cm (shorter side)
50 cm (longer side)
Step-by-step explanation:
Let the length of the shorter side of the parallelogram be x cm. Then, the length of the longer side is (2x + 20) cm. Since a parallelogram has opposite sides equal in length, there will be two shorter sides and two longer sides.
The perimeter of the parallelogram is given as 130 cm. The sum of the lengths of all four sides is equal to the perimeter. Therefore, we can set up the following equation:
2x + 2(2x + 20) = 130
Now, we can solve for x:
2x + 4x + 40 = 130
6x + 40 = 130
6x = 130 - 40
6x = 90
x = 90/6
x = 15
Now that we have found the length of the shorter side (x), we can find the length of the longer side:
Longer side = 2x + 20 = 2(15) + 20 = 30 + 20 = 50
So, the dimensions of the parallelogram are 15 cm (shorter side) and 50 cm (longer side).
The dimensions of the parallelogram are 15 cm x 50 cm.
What is a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure.
Given that, in a parallelogram, the longer side is 20 cm longer than twice the shorter side. the perimeter is 130 cm.
We need to find the dimension of the parallelogram,
Let the length of the shorter side of the parallelogram be x cm.
Then, the length of the longer side is (2x + 20) cm.
The perimeter of the parallelogram is given as 130 cm.
Therefore, we can set up the following equation:
2x + 2(2x + 20) = 130
Now, we can solve for x:
2x + 4x + 40 = 130
6x + 40 = 130
6x = 130 - 40
6x = 90
x = 90/6
x = 15
Longer side = 2x + 20 = 2(15) + 20 = 30 + 20 = 50
Hence, the dimensions of the parallelogram are 15 cm x 50 cm.
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a pentagon-shaped prism has bases with areas of 10 square feet each. it has rectangular sides with dimensions of 2 feet by 3 feet. find the total surface area.
Answer:
Step-by-step explanation:
What is a rectangular prism?
A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.
The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.
How do I find the volume of a rectangular prism?
The rectangular prism volume formula is:
volume = h × w × l,
where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:
Find the box length. For example, it can be equal to 18 in.
Determine its width. Let's say you measured 12 in.
Find out the rectangular prism height. Assume it's 15 in.
Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.
How do I find the area of a rectangular prism?
The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:
surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),
where h is prism height, w is its width, and l is its length.
Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:
Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².
Or save yourself some time and use our rectangular prism calculator.
Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.
How do I calculate the diagonal of a rectangular prism?
To determine the diagonal of a rectangular prism, apply the formula:
diagonal = √(l² + h² + w²)
where h is prism height, w is its width, and l is its length.
Do you have the feeling that you saw the formula before? Yes, that's possible because this equation resembles the famous one from the Pythagorean theorem.
9. Evaluate if p =-7, q = -2.
a. p + q
b. p - q
c. q - p
d.-p - q
Answer:
d
Step-by-step explanation:
trust me bro im a math teacher
POSSIBLE POINTS: 18.18
A sequence of transformations is applied to a polygon. Which of the following statements represent a sequence of transformations where the
resulting polygon is similar to the original polygon but has a smaller area than the original polygon? Select TWO that apply.
a reflection over the y-axis followed by a translation of 10 units down and a dilation about the origin by a scale factor of 2
a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5
units left
a rotation of 180° counterclockwise about the origin followed by a dilation about the origin by a scale factor of 5/2
a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y-axis and a dilation about the origin by a scale
factor of 3/4
Answer:
C, D
Step-by-step explanation:
Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.
C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left
D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4
HELP PLSSSS SSSSSSSS
Answer:A
Step-by-step explanation: i have had this question before
Answer:
A
Step-by-step explanation:
A proportion is given:
[tex] \frac{4}{5} = \frac{ {x}^{2} }{20} [/tex]
Use the property of proportion to find x (cross-multiply):
[tex]5 \times {x}^{2} = 20 \times 4[/tex]
[tex]5 {x}^{2} = 80[/tex]
Divide both sides of the equation by 5 to make x^2 the subject:
[tex] {x}^{2} = 16[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{16} = 4[/tex]
The radius of a circle is 13 in. Find its circumference in terms of \piπ.
[tex] \:\:\:\:\:\:\:\:\:\:\:\star\:\sf \underline{Circumference\: of\: circle = 2πr}\\[/tex]
As per question, the radius of a circle is 13 in and we are asked to find out it's circumference in terms of π. Here-
π = 3.1416...........Radius, r = 13 in.Now that we are given the value of radius of the circle, so we can substitute it into the formula and solve for circumference-
[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Circumference_{( circle)} = 2\pi r}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf Circumference_{( circle)} = 2 \times \pi \times 13\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Circumference_{( circle)} = 26 \pi \:inch}\\[/tex]
Therefore, the value of the circumference of the circle is 26π inch.The public library loaned out 25
mysteries, 10 non-fiction books, and
8 biographies on a random day.
Based on these results, how many
mysteries will be loaned out of the
next 301 books?
Answer: 175
Step-by-step explanation:
Lucy mode 256 neckloces. She used 16 beads on each neck-
lace. She sold the necklaces for $4 each. She spends $26 to
buy more beads. How much money does she have remaining?
A : $998
B : $1.024
C : $2,225
Answer:
A.998
Step-by-step explanation:
256 times 4 =1024-26=998 the facts that she uses 16 beads on each necklace is useless
I’m a certain magnetic field the cross-sectional area is 0.5 meter square and the flux is 1500 uwb what is the flux density
The flux density is 3000 uT.
Flux density (B) is a measure οf the strength οf a magnetic field in a given regiοn.
Hοw tο calculate flux density fοr the given prοblem?It is defined as the amοunt οf magnetic flux () that passes thrοugh a unit area (A) perpendicular tο the magnetic field's directiοn.
The flux density (B) can be calculated using the fοrmula:
B = Φ / A
where 'Φ' is -> flux and A is the -> crοss-sectiοnal area.
Plugging in the values given, we get:
B = 1500 uWb / 0.5 m²
B = 3000 uT (micrοtesla)
Therefοre, the flux density is 3000 uT.
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A diagonal is drawn on a square.
How many triangles are formed?
What is the sum of the measures of the angles of a triangle?
°
What is the sum of the angle measures of the square?
°
Answer:
2 triangles, 180 for each triangle and 360 degrees in a square