the number of fruit snacks in the bag is at least 18. Since each of the 3 people received no fewer than 6 fruit snacks, there must have been at least 18 fruit snacks in the bag for them to share equally.
What is inequality?Inequalities specify the connection between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equivalent. But various inequalities are used to compare the numbers and determine whether they are less than or greater than. Inequalities are the name given to these algebraic mathematical expressions.
Step-by-step explanation:
The inequality x divided by 3 ≥ 6 can be rewritten as x/3>=6, where x is the total number of fruit snacks in the bag.
To solve for x, we can multiply both sides of the inequality by 3 to isolate: x/3>=6x>=3*6x>=18
Therefore, the number of fruit snacks in the bag is at least 18. Since each of the 3 people received no fewer than 6 fruit snacks, there must have been at least 18 fruit snacks in the bag for them to share equally.
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Can someone please help
The volume of the cylinder is approximately 3,040π cubic centimeters.
How do you calculate a cylinder's volume?Cylinder volume V = A h.
As the formula for a circle's area is r2, the formula for a cylinder's volume is V = r² h.
We must apply the following formula to get the cylinder's volume:
V = πr²h
where V denotes the cylinder's volume, r denotes its radius, and h denotes its height.
The cylinder's height and radius are both claimed to be 15 centimetres and 8 cm, respectively. The formula produces the following outcomes when these values are added:
V = π(8 cm)²(15 cm) (15 cm)
V = π(64 cm²)(15 cm) (15 cm)
3,040 cubic centimeters equals V. (rounded to the nearest whole number)
As a result, the cylinder has a volume of about 3,040 cubic centimetres.
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Help me please I don't get it, it doesn't explain how to do it
The area of the shaded region is 15 [tex]yd^2[/tex].
What is area of the shape?The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Here in the given diagram contains right triangle and rectangle.
We need to find both triangle and rectangle area in order to find area of shaded region.
Now Base= 3+4 = 7 yd , Height h =6 yd. Then,
Area of triangle A = [tex]\frac{1}{2}bh[/tex] square unit
=> A = [tex]\frac{1}{2}\times7\times6[/tex]
=> A = [tex]7\times3 = 21 yd^2[/tex]
Now breadth b = 3 yd , Width w=2 yd, Then
Area of rectangle = bw square unit.
=> A = 3×2 = 6 [tex]yd^2[/tex]
Now area of the shaded region = Area of triangle - Area of rectangle
=> Area of shaded region = 21-6 = 15 [tex]yd^2[/tex].
Hence the area of the shaded region is 15 [tex]yd^2[/tex].
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Evaluate the integral below. ex dx SOLUTION The function f(x) = ex is continuous everywhere and we know that an antiderivative is F(x) = et, so Part 2 of the Fundamental Theorem gives | eа. ex dx = F(7) - F(5) = Notice that the Fundamental Theorem of Calculus says we can use any antiderivative Foff. So we may as well use the simplest one, namely F(x) = ex, instead of ex + 7 or ex + C.
To evaluate the integral of ex dx, we can use the Fundamental Theorem of Calculus, which states that if F(x) is an antiderivative of f(x), then the integral of f(x) from a to b is equal to F(b) - F(a).
In this case, the function f(x) = ex is continuous everywhere and we know that an antiderivative is F(x) = ex, so we can use this to evaluate the integral:
∫ex dx = F(7) - F(5) = e7 - e5
Notice that the Fundamental Theorem of Calculus says we can use any antiderivative F of f. So we may as well use the simplest one, namely F(x) = ex, instead of ex + 7 or ex + C.
Therefore, the integral of ex dx from 5 to 7 is equal to e7 - e5.
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in total there are 2022 kangaroos and some koalas living within seven parks. as many kangaroos live in each park as there are koalas in all other parks together. how many koalas in total live in the seven parks?
2022/(x-1) koalas in total live in the seven parks.
Let the number of parks be x.
According to the question, there are a total of 2022 kangaroos and some koalas living within seven parks.
Therefore, total number of kangaroos = 2022
Let the number of koalas in each park be y.
Number of koalas in each of the x-1 parks, other than the one with kangaroos = y
Number of koalas in the park with kangaroos = 2022/(x)
According to the question, there are as many kangaroos in each park as there are koalas in all other parks together.
So,Number of koalas in the park with kangaroos = y(x-1)2022/(x) = y(x-1)
Therefore, number of koalas in each of the x-1 parks = y = 2022/(x(x-1))
Total number of koalas living in seven parks = y
x= (2022/(x(x-1)))
x= 2022/(x-1)
Thus, the number of koalas in total live in the seven parks is 2022/(x-1).
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When an integer is subtracted from 2 times the next consecutive odd integer the difference is 9. Find the value of the greater integer
The value of the greater integer is 7 which is obtained by using arithmetic operations.
What are arithmetic operations?
It is claimed that all real numbers may be described by the four basic operations, sometimes known as "arithmetic operations". After division, multiplication, addition, and subtraction in mathematics are quotient, product, sum, and difference.
Let the integer be 'x'.
So, the next odd integer will be 'x + 2'.
We are given that when an integer is subtracted from 2 times the next consecutive odd integer the difference is 9.
So, from this we get
⇒2(x + 2) - x = 9
⇒2x + 4 - x = 9
⇒x + 4 = 9
⇒x = 5
The next integer will be 7.
Hence, the value of the greater integer is 7.
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please help. I'm not understanding.
The LCD of two fractions is the least common denominator that can be used to express both fractions as equivalent fractions with the same denominator.
The LCD can be found by listing the prime factors of the denominators, then finding the product of the prime factors that are shared by both denominators, as well as the prime factors that are not shared by either denominator.For example, the LCD of the fractions a/(bc) and (3x)/(b^2*y) is 4/(2x^3*y^2). The prime factorization of the denominators are bc=b*c, b^2*y=b^2*y, and 2x^3*y^2=2*x^3*y^2. The common prime factors between the denominators are b and y, and the prime factors that are not shared are c, x^3 and 2. The LCM of the denominators is therefore 2*b*y*x^3, which can be simplified to 4/(2x^3*y^2).By changing the denominators of the fractions to the LCM, equivalent fractions with the same denominators can be found. For example, for the fractions (2b + 3)/(b - 1) and (x + 4)/(x - 2), the LCD is (x - 2). The equivalent fraction with the denominator (x - 2) is (2b + 3x + 12)/(bx - 2).In a similar fashion, for the fractions (4y^2 - 7)/(y - 3) and (3x + 2)/(2x^2 + 9x + 4), the LCD is (2x^2 - 9y + 9). The equivalent fraction with the denominator (2x^2 - 9y + 9) is (8y^2 + 14x - 21)/(2x^3 - 27xy + 27x - 18y + 18).Finding the LCD of two fractions and changing the fractions to equivalent fractions with the same denominators is an important skill to master in order to solve fractional problems. By using the steps outlined above, it is possible to easily find the LCD and equivalent fractions.
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1. find the arc length of the following curves. then re-parameterize them by the arc length. (a) r(t)
The arc length parameterization of the curve r(t) = <sin(e^2t), cos(e^2t), e^2t> is: s(t) = t/2 [sqrt(t^2 + 1) + log(t + sqrt(t^2 + 1))]
To find the arc length parameterization of the curve r(t) = <sin(e^2t), cos(e^2t), e^2t>, we first need to find its speed, which is given by:
|v(t)| = sqrt[(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2]
= sqrt[(e^4t cos^2(e^2t)) + (e^4t sin^2(e^2t)) + e^4]
= sqrt[e^4t (cos^2(e^2t) + sin^2(e^2t)) + e^4]
= sqrt[e^4t + e^4]
= e^2 sqrt[t^2 + 1]
The arc length parameterization is given by s(t) = ∫|v(τ)|dτ from 0 to t. Substituting |v(t)|, we get:
s(t) = ∫e^2 sqrt[τ^2 + 1] dτ from 0 to t
This integral can be evaluated using a trigonometric substitution, u = τ/tan(theta), which gives:
s(t) = t/2 [sqrt(t^2 + 1) + log(t + sqrt(t^2 + 1))]
Therefore, the arc length parameterization is s(t) = t/2 [sqrt(t^2 + 1) + log(t + sqrt(t^2 + 1))].
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____The given question is incomplete, the complete question question is given below:
find the arc length parameterization of the curve
r(t)=<sin(e^2t),cos(e^2t),e^2t>
what is the circumference for something with a diameter of 5 inches
Answer:
15.7
Step-by-step explanation:
5 * 3.14 = 15.7
Answer:
Below
Step-by-step explanation:
CIRCUMFERENCE of a CIRCLE is given by : pi * d
Circumference = pi * 5 in = 15.7 inches (Don't forget UNITS !!)
f(x)= x + 5 + x^3 even , odd , or neither .
Answer: x = ∛5. This is even. If the answer is wrong I'm sorry.
Step-by-step explanation:
pls help me this is due now 30 points for it!
Teresa has two 6-foot pieces of ribbon. One piece she cuts into 1/4 foot pieces.The other piece she cuts into 1/2-foot pieces. How many 1/4 pieces can she cut from one piece of ribbon?Explain please help.
In the wοrd prοblem, 24 pieces οf 1/4 pieces can she cut frοm οne piece οf ribbοn.
What is wοrd prοblem?Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.
Here the tοtal length οf οne piece οf ribbοn = 6 fοοt.
Length οf οne piece she cuts = 1/4 fοοt.
Number οf 1/4 pieces frοm οne piece = Tοtal length/ One piece length
=> [tex]\frac{6}{\frac{1}{4}}[/tex]
=> [tex]6\times4[/tex]
=> 24 .
Hence 24 pieces of 1/4 pieces can she cut from one piece of ribbon.
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At a factory, two machines pack bottles into boxes for shipping. Machine A can pack 8 boxes per minute, and Machine B can pack 11 boxes per minute. Before shipment, an inspector found that 7 of the boxes packed by Machine A were defective and could not be shipped. At least 200 boxes packed by Machine A were approved for shipment. Write and solve an inequality to find the amount of time Machine A spent packing the boxes that were approved for shipment.
(different from last question
After answering the given query, we can state that Therefore, Machine A inequality the boxes that were authorized for shipment in at least 25.875 minutes (or roughly 26 minutes).
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Thus, disparity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and disparity are not the same. Use the not equal sign most frequently when two values are not identical. (). Values of any size can be contrasted using a variety of disparities. By changing the two sides until only the factors are left, many straightforward inequalities can be solved. However, a number of factors support inequality: Both parts' negative values are divided or added. Exchange the left and the right.
Let's indicate how long Machine A took to pack the boxes that "t" had given the go-ahead to send. (in minutes).
Machine A packed 8 boxes per minute during this period, for a total of 8t boxes.
8t - 7 ≥ 200
The reality that this inequality exists indicates that Machine A (8t - 7) must pack more than 200 approved boxes.
We can first add 7 to both sides of the equation before attempting to solve for "t":
8t ≥ 207
Next, multiply both ends by 8:
t ≥ 25.875
Therefore, Machine A packed the boxes that were authorized for shipment in at least 25.875 minutes (or roughly 26 minutes).
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which is a value of 60 = cos(x + 10)?
[tex]\displaystyle \sf sin(60^\circ) = cos(x+10^\circ) \\\\ \text{we now that} : \\\\ sin(90^\circ-\theta) = cos(\theta) \\\\\ therefore : \\\\ sin(90^\circ-30^\circ) = sin(60^\circ) = cos(30^\circ)\\\\\\\ \text{So}: \\\\ cos(30^\circ) = cos(x+10^\circ) \\\\ 30^\circ = x+10^\circ \\\\ \large\boxed{\sf \ x = 20^\circ\ }\checkmark \\\\\ \text{or } \\\\ x = 20^\circ +2\cdot k \cdot \pi \ \ \ ;\ (k\in \mathbb{Z} )[/tex]
Find the area of the circle below (round to the nearest tenth)
Answer: _____yd2
The area of the circle below (round to the nearest tenth) is A ≈ 113.1 [tex]yd^2.[/tex]
Why is the radius of a circle r 2?The usual definition of pi is the ratio of a circle's circumference to its diameter, so that a circle's circumference is pi times the diameter, or 2 pitimes the radius.
Use the following formula to calculate the area of a circle:
A = πr²
where A is the circle's area, (pi) is a constant approximately equal to 3.14, and r is the circle's radius.
The diagram shows that the circle's diameter is 12 yards, so the radius is half that, or 6 yards. We get the following when we substitute into the formula:
A = 3.14(6²) \s≈ 113.1 yd²
We get the following when we round to the nearest tenth:
A ≈ 113.1 yd².
A = πr²
where A is the circle's area, (pi) is a constant approximately equal to 3.14, and r is the circle's radius.
The diagram shows that the circle's diameter is 12 yards, so the radius is half that, or 6 yards. We get the following when we substitute into the formula:
A = 3.14(6²) \s≈ 113.1 yd²
We get the following when we round to the nearest tenth:
A ≈ 113.1 yd²
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Select the expression that represents the following statement: add 24 to the quotient of 16 and 8. (2 points)
Group of answer choices
16 x 8 + 24
(16 ÷ 8) + 24
24 − 8 + 16
(16 − 8) + 24
The expression (16 ÷ 8) + 24 evaluates to 26 and represents the statement “add 24 to the quotient of 16 and 8”.
The expression that represents the statement “add 24 to the quotient of 16 and 8” is (16 ÷ 8) + 24.
To solve this expression, we will use the order of operations (PEMDAS). First, we will calculate the quotient of 16 and 8. To do this, we will divide 16 by 8.
16 ÷ 8 = 2
Then, we will add 24 to the result of the division.
2 + 24 = 26
Therefore, the expression (16 ÷ 8) + 24 evaluates to 26.
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(1.13) The experiment is to select a person from the U.S. at random. Event A is "person resides in New York" and Event B is "person is an immigrant." Suppose P(A) = 0.066, P(B) = 0.072, and P(An B) = 0.02. (a) Interpret the events An B and AUB. (b) What is P(AUB)?
The probability of selecting someone from the U.S. who either resides in New York or is an immigrant is 0.118.
Interpret the events An B and AUB:An event An B refers to the occurrence of the event A as well as event B happening together. The person being selected is an immigrant and also resides in New York. The probability of this happening is 0.02. On the other hand, AUB refers to the probability of selecting a person who either resides in New York or is an immigrant.
What is P(AUB)?For AUB, we need to calculate the probability of selecting someone from the U.S. who either resides in New York or is an immigrant. In probability, the general formula to calculate AUB is: P(AUB) = P(A) + P(B) - P(An B)Substituting the values given in the problem statement: P(AUB) = 0.066 + 0.072 - 0.02 = 0.118 Therefore, the probability of selecting someone from the U.S. who either resides in New York or is an immigrant is 0.118.
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In a triangle ABC, c=16cm,a=10cm and B =125 degrees Calculate the remaining angles and sides
Answer:
the remaining angles are A ≈ 26.8 degrees and C ≈ 28.2 degrees, and the remaining side is b ≈ 13.96 cm.
Please help and explain.
Answer:
R = 13 cm, x = 5 cm
Step-by-step explanation:
We can see, that AO = BO = EO
First, we have to find AO from ∆OAD by using the Pythagorean theorem:
[tex] {ao}^{2} = {ad}^{2} + {x}^{2} [/tex]
[tex] {ao}^{2} = 144 + {x}^{2} [/tex]
[tex]ao > 0[/tex]
[tex]ao = \sqrt{144 + {x}^{2} } [/tex]
Now, let's write that EO = (8 + x)
Since AO = EO, we can write an equation:
[tex] \sqrt{144 + {x}^{2} } = 8 + x[/tex]
Let's square the whole equation:
[tex]144 + {x}^{2} = ( {8 + x})^{2} [/tex]
[tex]144 + {x}^{2} = 64 + 16x + {x}^{2} [/tex]
[tex] {x}^{2} - {x}^{2} - 16x = 64 - 144[/tex]
[tex] - 16x = - 80[/tex]
Let's divide both sides of the equation from -16:
[tex]x = 5[/tex]
OB = 8 + x = 8 + 5 = 13 (radius)
a man with blood type a has a child with a woman also of blood type a. what is the probability their child has bloodtype a g
A man with blood type A has a child with a woman also of blood type A. The probability that their child will have blood type A is 100%.
There are four different blood types: A, B, AB, and O. Each person has two copies of the gene that determines their blood type, one from their mother and one from their father.
The probability of a child inheriting a certain blood type depends on the blood types of the parents.
If they both have the IAIA genotype, then their child will definitely have blood type A, since they will inherit one copy of the A allele from each parent.
If they both have the IAi genotype, then there is a 50% chance that their child will have blood type A and a 50% chance that their child will have blood type O (since the i allele is recessive and will not express its phenotype unless both alleles are i).
However, since we know that both parents in this scenario have blood type A, then we can conclude that they both have the IAIA genotype.
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Sara drives 72 miles on 3.2 gallons of gas. She uses this information to calculate how many miles per gallon she can drive. Using this result, how many miles can Sara drive on 13.3 gallons of gas?
Answer:
299 miles
Step-by-step explanation:
Set a proportion:
72 miles : 3.2 gallons = x miles : 13.3 gallons
x = (72 × 13.3) ÷ 3.2 = 299 miles
Answer:
Step-by-step explanation:
i think its 230.4
1. Suppose it is known from large amounts of historical data that X, the number of cars thatarrive at a specific intersection during a 20-second time period, is characterized by thefollowing discrete probability function:ƒ(x) = e−6. 6x/x!for x = 0,1,2,. Find the probability that in a specific 20-second period,less than 3 cars arrive at the intersection.between 2 and 4 (both inclusive) cars arrive at the intersection.
The probability that between 2 and 4 cars arrive at the intersection during a 20-second period is 0.1317.
To find the probability that in a specific 20-second period, less than three cars arrive at the intersection, we need to sum up the probabilities of the possible outcomes for x = 0, 1, and 2.
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]e^{-6.60}/0! + e^{-6.61}/1! + e^{-6.6\times2}/2![/tex]
= 0.0018 + 0.0119 + 0.0311
= 0.0448
Therefore, the probability that less than three cars arrive at the intersection during a 20-second period is 0.0448.
To find the probability that between 2 and 4 cars arrive at the intersection, we need to sum up the probabilities of the possible outcomes for x = 2, 3, and 4.
P(2 ≤ X ≤ 4) = P(X = 2) + P(X = 3) + P(X = 4)
=[tex]e^{-6.62}/2! + e^{-6.63}/3! + e^{-6.6\times4}/4![/tex]
= 0.0311 + 0.0482 + 0.0524
= 0.1317
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Hugo is serving fruit sorbet at his party. he has 1 gallon of fruit sorbet to serve to 32 friends. if each person receives the same amount, how many cups of fruit sorbet will each person get? 14 cup 12 cup 34 cup 1 cup
If each person receives the same amount, each person at Hugo's party will get 0.5 cups, or 1/2 cup, of fruit sorbet.
To determine how many cups of fruit sorbet each person will get, we need to convert the volume of the sorbet from gallons to cups, and then divide by the number of people who will be served.
Since 1 gallon is equal to 16 cups, we can multiply the number of gallons by 16 to get the total number of cups of sorbet. In this case, 1 gallon x 16 cups/gallon = 16 cups of fruit sorbet.
To find out how many cups of sorbet each person will get, we simply divide the total number of cups by the number of people. In this case, 16 cups ÷ 32 people = 0.5 cups/person.
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discussion forum 3 questions : what is an yoield curve? what are the differet shapes the yield curve can take? explain.
The yield curve is an important tool for understanding the relationship between short-term and long-term interest rates, and the different shapes it can take provide insight into the market's expectations for the economy and interest rates.
A yield curve is a graph that plots the yields of similar-quality bonds against their maturities, ranging from shortest to longest. It is used to understand how the market is anticipating changes in interest rates and the economy.
The yield curve can take on different shapes, depending on the relationship between short-term and long-term interest rates. The three main shapes of the yield curve are:
Normal yield curve: This is when long-term yields are higher than short-term yields, indicating that investors expect the economy to grow and inflation to increase in the future.
In conclusion, the yield curve is an important tool for understanding the relationship between short-term and long-term interest rates, and the different shapes it can take provide insight into the market's expectations for the economy and interest rates.
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Describe how to construct the Riemann surfaces for the following functions: (a) w = z ^ (1/4) , (b) w = √zi, (c) w = (z - 1) ^ (2/5) Remark. To describe the Riemann surface of a multivalued function, begin with one sheet for each branch of the function, make branch cuts so that the branches are defined continuously on each sheet, and identify each edge of a cut on one sheet to another appropriate edge so that the function values match up continuously.
The Riemann surface visualizes complex functions with multiple values using sheets and branch cuts for continuity and clarity.
(a) w = z^(1/4)The Riemann surface of w = z^(1/4) is constructed in the following manner:
One sheet is designated for each of the four roots. To avoid ambiguity, each sheet is colored differently.Then, in order to make the branches continuous on each sheet, a branch cut is created along the negative real axis (as shown below).Finally, the sheets are matched up using the edges of the cut as boundaries, so that the function values are continuous.
(b) w = √ziTo construct the Riemann surface for w = √zi, the following steps are taken:
(c) w = (z - 1)^(2/5)The following steps are taken to construct the Riemann surface for w = (z - 1)^(2/5):
By designating sheets for each root and creating branch cuts along appropriate intervals, the Riemann surface ensures continuity and clarity in the representation of these functions.
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[100 POINTS!!!] Given the graph below. Label each part as follows:
1. Highlight the Max Point in Red
2. Highlight the Min Point in Yellow
3. Highlight the x-intercept(s) in Green
4. Highlight the y-intercept in Blue
Step-by-step explanation:
The Max point is the highest point on the arc.
The Min point is the lowest point on the arc.
The x-intercepts are the places where y = 0, and the graph crosses the x-axis.
The y-intercepts are the places where x = 0, and the graph crosses the y-axis.
Post this question to forum Bryce runs a 100 meter race. 5 seconds after the race started Bryce is 45 meters from the starting line and reaches his max speed, he runs at this max speed for the rest of the race. Bryce notices that he is 77 meters from the starting line 9 seconds after the race started. a What is Bryce's max speed? meters per second Preview b. Suppose Bryce runs for an additional z seconds after reaching his max speed.. i How far will Bryce travel during those additional z seconds? (Preview; ii What is Bryce's distance from the starting line 5+ z seconds after the race started? meters # meters Preview c. What is Bryce's distance from the starting line z seconds after the race started (provided z 2 5)? meters Preview Submit Question 4. Points possible: 4 Unlimited attempts Score on last attempt 1. Score in gradebook: 1 Message instructor about this question & Ucense
The Bryce's distance from the starting line z seconds after the race started (provided z ≤ 5) will be (45 + 11z) meters.
Bryce runs a 100 meter race. 5 seconds after the race started Bryce is 45 meters from the starting line and reaches his max speed, he runs at this max speed for the rest of the race. Bryce notices that he is 77 meters from the starting line 9 seconds after the race started. Find the max speed and distance. a) Bryce's max speed = 11 meters per secondb) Bryce travels (11z) meters during the additional z seconds.
Bryce's distance from the starting line 5+ z seconds after the race started will be (45 + 11z) meters.c) Bryce's distance from the starting line z seconds after the race started (provided z ≤ 5) will be (45 + 11z) meters.Explanation:The problem deals with a boy named Bryce, who runs 100 meters and reaches his maximum speed.
Let the max speed be v m/s, and the time he runs at the max speed be t seconds.From the problem, Bryce is 45 meters from the starting line 5 seconds after the race started. And Bryce notices that he is 77 meters from the starting line 9 seconds after the race started.
The solution of the problem is as follows: The max speed can be found using the formula as follows:S = ut + (1/2)at²Here, initial velocity u = 0, final velocity v = v m/s, t = t seconds, S = distance traveled by Bryce in t seconds, a = acceleration of Bryce. Let the distance Bryce travels at maximum speed be x meters, and he takes t seconds to cover the distance.
Thus,x = v × t ... (1)Also, the distance Bryce travels during the first 5 seconds is 45 meters. Thus, using the equation of motionS = ut + (1/2)at² and putting a = 0, we have45 = 0 × 5 + (1/2) × 0 × 5² = 0 + 0 = 0Or, S = ut + (1/2)at² = 45 meters ... (2)Now, let the additional time be z seconds. Thus, the total time Bryce runs will be t + z seconds. Now, the distance Bryce travels will be (45 + x) meters + v × z meters.
Let the distance Bryce travels during z seconds be y meters. Thus,y = v × z ... (3)Therefore, the total distance traveled by Bryce will be(45 + x) meters + v × z meters = (45 + x + y) metersAlso, the total time taken to run the race will be (t + z) seconds.
Now, using the equation of motionS = ut + (1/2)at² and putting S = 77 meters, t = 5 seconds and a = 0, we have77 = 0 × 5 + (1/2) × 0 × (5 + z)² + x + v × z = x + v × z ... (4)Thus, from equations (1) and (4), we getv = (77 - 45)/z ... (5)Using equation (3) and the value of v from equation (5), we can find the distance traveled by Bryce in additional time z seconds.
Thus,y = v × z = (77 - 45)/z × z = 32 metersThus, the total distance traveled by Bryce will be(45 + x) meters + v × z meters = (45 + x + 32) meters = (77 + x) metersUsing equation (2), we have45 = 0 × 5 + (1/2) × 0 × 5² = 0 + 0 = 0Or, S = ut + (1/2)at² = 45 meters ... (2)Therefore, Bryce's distance from the starting line z seconds after the race started (provided z ≤ 5) will be (45 + 11z) meters.
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You have $3.35 in dimes and quarters.
You have 17 coins total. How many are dimes and how many are quarters?
a. 6 quarters, 11 dimes
b. 7 quarters, 10 dimes
c. 11 quarters, 6 dimes
d. 10 quarters, 7 dimes
Answer: c
Step-by-step explanation: .25 +.25 + .25 +.25 + .25 +.25 + .25 +.25 + .25 +.25 + .25 + .60=3.35
geometry, i don’t understand
Answer:
24
Step-by-step explanation:
its saying the total of the area
A jar contains 76 more pennies than nickels.
The total value of the pennies equals the
total value of the nickels.
a) How many nickels are there?
b) What is the total value of all the coins in
the jar?
The tοtal value οf all the cοins in the jar is $1.90.
Let's start by setting up sοme equatiοns based οn the infοrmatiοn given in the prοblem:
Let's call the number οf nickels "n".
Then the number οf pennies must be "n + 76".
The value οf "n" nickels is 0.05n dοllars.
The value οf "n + 76" pennies is 0.01(n + 76) = 0.01n + 0.76 dοllars.
Since the tοtal value οf the pennies equals the tοtal value οf the nickels, we can set up an equatiοn:
0.05n = 0.01n + 0.76
Simplifying this equatiοn, we get:
0.04n = 0.76
n = 19
Sο there are 19 nickels in the jar.
Tο find the tοtal value οf all the cοins, we can use the fact that the value οf "n" nickels is 0.05n dοllars and the value οf "n + 76" pennies is 0.01n + 0.76 dοllars:
Tοtal value = (0.05n) + (0.01n + 0.76)
= (0.05 x 19) + (0.01 x 19 + 0.76)
= 0.95 + 0.95
= 1.90
Sο the tοtal value οf all the cοins in the jar is $1.90.
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Circle the expression that does not belong with the other three. Explain.
1/2×12
9×2/3
1/4×20
1/6×36.
After answering the given query, we can state that As a result, 1/4 20 is the expression that does not fit with the other three.
what is expression ?In mathematics, you can multiply, split, add, or take away. The following is how an expression is made together: Numeric value, expression, and arithmetic operator The elements of a mathematical expression are integers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical declaration containing variables, numbers, and a mathematical action between them is known as an expression, also known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the provided equation, which are all separated by the mathematical symbol +.
1/420 is the phrase that doesn't fit with the other three.
The other three statements all translate to 6:
1/2 × 12 = 6
9 × 2/3 = 6
1/6 × 36 = 6
Nevertheless, 1/4 x 20 = 5.
As a result, 1/4 20 is the expression that does not fit with the other three.
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