Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.
What is Time, Speed and Distance?Time is the duratiοn between twο events, speed is the rate at which distance is cοvered per unit time, and distance is the amοunt οf space between twο οbjects οr pοints.
Sylvia has cοmpleted the first 5 laps in a tοtal time οf 5 x 73 secοnds = 365 secοnds.
Tο break the natiοnal recοrd οf 14 minutes 35 secοnds (οr 875 secοnds) fοr running 5000m, Sylvia has 5000m - 5 laps (οf 400m each) = 3000m remaining tο run, which is equivalent tο 7.5 laps (since each lap is 400m).
Let's say Sylvia needs tο cοmplete the remaining 7.5 laps in x secοnds.
Tο break the natiοnal recοrd, the tοtal time fοr running 12.5 laps (οr 5000m) shοuld be 875 secοnds οr less. Sο, we can set up the fοllοwing equatiοn tο find the required average lap time fοr the remaining 7.5 laps:
365 secοnds + 7.5x secοnds ≤ 875 secοnds
Subtracting 365 secοnds frοm bοth sides gives:
7.5x secοnds ≤ 510 secοnds
Dividing bοth sides by 7.5 gives:
x secοnds ≤ 68 secοnds
Sο, Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.
Therefοre, the answer is 68 secοnds.
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Rachel bought three and fifty-two hundred pounds of apples at the store. How is this written in number form?
3.0052
3.052
3.502
3.52
Answer: 3.52
Step-by-step explanation: fifty-two hundredths as a number would be 0.52, so 3.00 + 0.52 would be 3.52
AB (3x + 2) cm AC 11 cm BC (2y + 3) In the diagram, ABC is an equilateral triangle. Find the value of (x+y)
For the given triangle ΔABC the value of (x + y) would be 7 cm.
What is an equilateral triangle?
An equilateral triangle is a triangle with the same length on all three sides. An equilateral triangle is also equiangular in Euclidean geometry; that is, all three internal angles are congruent to each other and are each 60°.
Given data:
Length of AB = (3x + 2) cm.
Length of AC = 11 cm.
Length of BC = (2y + 3) cm.
The property of an equilateral triangle says that all sides of an equilateral triangle are equal.
then we can write,
AB = AC
3x + 2 = 11
3x = 11 - 2
3x = 9
x = 9/3
x = 3 cm
Also, BC = AC
2y + 3 = 11
2y = 11 - 3
2y = 8
y = 8/2
y = 4 cm
So the value of (x + y) = 3 +4
= 7 cm.
Hence, For the given triangle ΔABC the value of (x + y) would be 7 cm.
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3) Justin made some cookies for the holiday. She baked 10 sugar cookies, 18 chocolate chip cookies, and 15 ginger cookies. What is the ratio of sugar cookies to ginger cookies in simplest form?
Solve for an angle in right triangles
I just need the answer i don’t need the whole thing explained :)
Answer: ∠B≈39.81°
Step-by-step explanation:
[tex]\displaystyle\\tg\angle B=\frac{AC}{BC} \\\\tg\angle B=\frac{5}{6} \\\\\angle B=arctg\frac{5}{6} \\\\\angle B\approx39.81^0[/tex]
javieretta earned $9.50 each hour she works at camp clap happy during summer vacation. she earned $304 one week in june and $247 during a week in july. how many hours did she work that week in june? please help
Javieratta worked for a total of 32 hours in the week of June to earn an amount of 304 dollar.
Javieretta earns $9.50 each hours she works at camp clap happy.
She earned $304 in week of june and $247 during a week in july.
Let us assume that she works X hours.
So, using unitary method, we can write,
X times the amount she earns in one hour = Earning in the week of june.
X(9.50) = 304
X = 304/9.50
X = 32 hours.
So, she worked for a total of 32 hours in the camp clap happy summer vacation.
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precipitation data was compiled and discretized into three states. 1. dry, 2. light rain, and 3. wet. given these states the tratisition matrix chain model of davis rainfall was computed as. what is the probability a dry day is followed by a light rain day
The probability a dry day is followed by a light rain day is 0.07.
Define probability.Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Given.
Here, the markov chain's three possible states are listed as dry, light rain, and wet.
From the second number in the first row, the chance of a dry day followed by a light rain is calculated as follows: P(dry⇒ light) = 0.01.
Therefore, the necessary probability in this case is 0.01.
We currently have (wet⇒ light) - 0.07
Therefore, the necessary probability in this case is 0.07.
The probability a dry day is followed by a light rain day is 0.07.
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A bad contains 7 red marbels and 4 blue marbles
A marble is taken from the bag and replaced
another marble is taken from the bag
Work out the probability that the two marbles are the same colour
Give your answer as a fraction
Answer:
I think its 7/3 or 6/4
Step-by-step explanation:
Answer:
Step-by-step explanation:
(a) Because there are 7 red and 4 blue marbles, there are 7+4=11 marbles in the bag.
So the ratio of all marbles to blue marbles is 11 to 4.
We write this as follows. 11:4
(b)There are 7 red marbles and 4 blue marbles in the bag.
So the ratio of red marbles to blue marbles is 7 to 4.
We write this as follows. 7:4
Graph the inequality on the axes below −2x+y≥−6
A graph of the inequality (-2x + y ≥ -6) is shown in the image attached below.
What is a graph?A graph simply refers a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.
Next, we would rearrange and simplify the given equation in slope-intercept form as follows:
-2x + y ≥ -6
Adding 2x to both sides of the inequality, we have the following equation:
-2x + y + 2x ≥ -6 + 2x
y ≥ -6 + 2x
Rearranging the equation in slope-intercept form, we have the following equation:
y ≥ 2x - 6
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Find the slope of the line between the given points.
(2,5) and (3,8)
Answer: m (slope) = 3
Step-by-step explanation: Slope Solution
m=rise run=ΔyΔx
m=y2−y1x2−x1
m=8−53−2
m=31
m = 3
Point Slope Form
y−y1=m(x−x1)
y−5=3(x−2)
Slope Intercept Form
Find the Equation of the Line:
y=mx+b
by solving for y using the Point Slope Equation.
y−y1=m(x−x1)
y−5=3(x−2)
y−5=3x−(3×2)
y−5=3x−6
y=3x−6+5
y=3x−1
m=3
b=−1
Hope this helps :)
Rewrite the equation in Ax+By = C form. Use integers for A, B, and C. y+3=-4(x-6)
Answer:
4x + y = 21
Step-by-step explanation:
1. distribute in the parenthesis first, so the right side of the equation is not -4x+24
Right now the total equation looks like y+3 = -4x+24
2. Now we add the 4x to both sides to cancel it out on the left side, so we're left with:
4x+y+3=24
3. After that we can subtract the 3 from both sides to leave us with:
4x+y=21
It’s time for ronda to start repaying her student loans, which are amortized over the next 10 years, her first payment due is $396 how much should she expect to pay next month
Based on the amount that she paid in the first month, the amount Ronda will pay for the next month is $396.
When a loan is amortized, it means that one can pay it off by paying the same amount every period until they would have paid off both the loan and the associated interest.
The amortized amount contains:
A portion going towards the principal(debt )
A portion going towards the interest accumulated.
In conclusion, as the amount is the same every time, Ronda will have to pay the same amount of $396 the next month.
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A line has a slope of -7 and includes the points (-2, -10) and (-3, h). What is the value of h?
Answer:
-3
Step-by-step explanation:
You can use to find the slope of a line going through and .
I like to line up the points and subtract vertically. Then put 2nd difference over 1st difference.
(6,h)
minus
(7,-10)
------------
-1 h-(-10)
This also said to be equal to -7:
Multiply -1 on both sides:
Subtract 10 on both sides:
[texh=-3[/tex]
So if h=-3 then the slope of the line going through (6,h) and (7,-10) is -7.
Let's test it:
(6,-3)
minus
(7,-10)
----------
-1 7
So the slope is 7/-1=-7. This is the intended goal.
The check is good.
A Pre-K teacher has a total of 4/5 ounces of paint. Th teacher puts 1/30 ounces of paint at each table. If the teacher sets up an equal number of tables in the 2 Pre-K classrooms, how many tables does he set up in each classroom?
Answer:
12 tables per classroom.
Step-by-step explanation:
We will assume that the teacher uses all of the 4/5 oz of paint. We can find how many samples of 1/30 oz are contained in the 4/5 oz by dividing:
(4/5)÷(1/30) = (4/5)*(30/1)
(4/5)*(30/1) = (120/5)
(120/5) = 24 samples of 1/30 oz paint in (4/5) oz total paint.
Each of the 2 Pre-K classrooms have the same number of tables, so we can divide 24 samples by 2 to find the number of tables in each classroom,
*24 samples/2 classrooms) = 12 tables/classroom
Given g(x)=-x-4g(x)=−x−4, solve for xx when g(x)=10g(x)=10.
The solution for x in the function when the function g(x) = 10 is 4
How to determine the solution for x in the function?From the question, we have the following equation that can be used in our computation:
g(x)=x-4
To make the equation legible, we need to rewrite it
So, we have the following representation
g(x) = x - 4
Also from the question, we have
g(x) = 10
This means that we calculate x when g(x) = 10
Substitute the known values in the above equation, so, we have the following representation
10 = x - 4
So, we have the following equation
x - 4 = 10
Add 4 to both sides of the equation
So, we have the following representation
x - 4 + 4 = 10 + 4
Evaluate the equation
x = 14
Hence, the solution is 14
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Select the graph that can be used to find the solution(s) of the system of equations:
y = |x| – 3
y = –x2 + 9
Answer:
(3,0) (-3,0)
Step-by-step explanation:
ask:))
A bakery sold a total of 3028 coffee and blue berry buns.1560 more coffee buns were sold than blue berry buns.how many coffee buns did the bakery sell
Answer:
the bakery sold 1468 blueberry buns sooooo yeah
Step-by-step explanation:
Write the equation for the absolute value function graphed
Thank you!
The equation using the absolute value function is x+2y-8=0.
What is an Absolute Value Function?The graph opens up or down depending on the value of variable a, which also indicates how far it stretches vertically.We can determine the graph's horizontal and vertical shifts using the variables h and k.The general form of the Absolute value function is f(x) = a|x-h| + k.In the given graph, we have:
(h, k) ∈ (4, 2) and a = -1/2
In the general absolute value function, substitute these values:
Let's f(x) be y:
y = a | x - h | + k= (-1/2) |x-4| + 2 = (-x/2) + (4/2) +2 = -x/2 + 4 (Multiply with 2)2y = -x + 8x + 2y - 8 = 0Therefore, the equation using the absolute value function is x+2y-8=0.
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please answer this question (answer is needed as a fraction)
Answer:
4/6 means 2/3 it is most likely 0, 67 or 0, 66.
Step-by-step explanation:
the p-value is a. a sample statistic. b. the same as the z statistic. c. a distance. d. a probability.
The p - value is d ) a probability .
Defining P - Value
P - Value : It is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test , assuming that the null hypothesis is correct . The p - value does not , in itself , establish probabilities of hypotheses . Rather , it is a tool for deciding , whether to reject null hypothesis or not .
A smaller p - value means that there is stronger evidence in favor of alternative hypothesis .
Hence , the p - value is d ) a probability .
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would appreciate getting the answer
The value of angle 5 is 115°
What are corresponding angles?Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).
angle 2 is 65°
angle 6 = angle 2 = 65°( corresponding angles)
angle 6 + angle 5 = 180( angles on a straight line)
65 + angle 5 = 180
angle 5 = `180 - 65
angle 5 = 115°
In conclusion, angle 5 is 115°
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iq test scores are normally distributed with a mean of 100 and a standard deviation of 15. an individual's iq score is found to be 90. find the z-score corresponding to this value.
The Z score of the individual with IQ 90 is -0.67.
It is given that the scores are Normally distributed.
The mean given is 100 while the standard deviation is 15.
Let the IQ distribution be X.
Hence X follows a Normal distribution X~N(100, 225)
where
100 = mean
225 = standard deviation
To find the Z score we need to convert the following into the standard normal distribution.
To do that we need to follow
Z = ((x - μ) / σ)
here
μ = mean of the distribution = 100
σ = standard deviation of the distribution = 15
x = 90
Hence the Z score is
Z = (90 - 100) / 15
= -10/15
= -0.67
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Jada is working on solving a quadratic equation, as shown here.
p^2−5p=0
p(p−5)=0
p−5=0
p=5
She thinks that her solution is correct because substituting 5 for p in the original expression p^2−5p gives 5^2−5(5), which is 25−25 or 0.
Explain the mistake that Jada made.
Writing only p = 5 is a mistake since p = 0 is also a solution of the quadratic equation
How to find the mistake she made in solving the quadratic equation?
Given the quadratic equation: p² −5p = 0
p² −5p = 0
p(p−5) = 0
p = 0 or p−5=0
p = 0 or p = 5
Jada made mistake in the 3rd step instead of him to break the equation into two parts and then equate them to zero i.e he neglected the part where p = 0 and only make use of p-5 = 0
Since the equation has two solutions, p = 0 and p = -5. Therefore, writing only p = 5 is a mistake because when p = 0 is substituted into p² −5p = 0, it also gives 0
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Write an expression to represent:
4 times the difference of x and 2.
Answer:
4 times the difference of x and 2 is 4(x-2)
Zach took a science test. He answered 42 questions correctly and 8 questions incorrectly.
What percentage of the questions did Zach answer correctly?
Answer:
84%
Step-by-step explanation:
correct answers = 42
incorrect answers =8
total mark=50
% of the correct =
[tex] \frac{42}{50} \times 100 = 84[/tex]answer is 84%
Shipping Company A charges $14 plus $2.25 a pound to ship overnight
packages. Shipping Company B charges $20 plus $1.50 a pound to ship
an overnight package. For what weight is the charge the same for the two
companies?
For 8 pounds of weight, the charges be the same for both the companies.
Given, that To ship an overnight package
Shipping Company A charges $14 plus $2.25 per pound
Shipping Company B charges $20 plus $1.50 per pound
Let, the weight be w
And the cost of shipment by company A & B be A(w) & B(w) respectively.
According to the question,
A(w) = 14 + 2.25w
B(w) = 20 + 1.50w
Now, when charges be the same
A(w) = B(w)
14 + 2.25w = 20 + 1.50w
On subtracting 1.50w on both the sides, we get
14 + 2.25w - 1.50w = 20 + 1.50w - 1.50w
14 + 0.75w = 20
Now on subtracting 14 on both the sides, we get
14 + 0.75w - 14 = 20 - 14
0.75w = 6
On dividing both the sides by 0.75, we get
0.75w/0.75 = 6/0.75
w = 8
Hence, weight = 8 pounds.
For 8 pounds of weight, the charges be the same for both the companies.
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Here is a rectangle.
5 cm
7 cm
5 cm
7 cm
The 6-sided shape is made from two of these rectangles.
Work out the perimeter of this 6-sided shape.
The perimeter of the rectangle is = 48cm
What is permeter of rectangle?The overall length of the outline determines a shape's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter. The rectangle's perimeter can be expressed as the product of its length and width times two. As a linear measurement, the perimeter can be expressed in meters, centimeters, inches, feet, etc.Acc to our question-
area: 7x5 cm, or 357cm + 7cm + 5cm + 5cm = 24simply add two rectanglesarea35+area35:area70perimeter24+perimeter24:perimeter48Hence,The perimeter of the rectangle is = 48cm.
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-6 > v + 3/5 solve for the inequality for v and simplify your answer as much as possible
Answer: -33/5
Step-by-step explanation:
5/6 divided by
(- 13/7)
PLEASE HELP, NEED ASAP
Answer:
Step-by-step explanation:
help meeeeeeeeeeeeeeeeee please
Answer:
t=0
Step-by-step explanation:
Your equation would be 324=-16t^2+324 since 370-46 is 324. subtract each side by 324 and you get 0=-16t^2. t=0