Answer:
Average speed = 3848 km / h
Step-by-step explanation:
Given:
It took Thandile 30 minutes to fly the distance of 1924 km between Pilanesburg National Park and Johannesburg.
To find:
Calculate the average speed.
Solution:
Average speed = distance / time
30 min = 0.5 h => 1924 / 0.5
= 3848 km / hours
Answer:
Average speed = 3848 km / h
hope this helps.....
Xavier shoots a basketball in which the height, in feet, is modeled by the equation,h(t) = -4t2 + 10 + 18, where t is time, in
seconds. What is the maximum height of the basketball?
Answer:
The maximum height of the basketball is of 24.25 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Height of the basketball:
Given by the following function:
[tex]h(t) = -4t^2 + 10t + 18[/tex]
Which is a quadratic function with [tex]a = -4, b = 10, c = 18[/tex]
What is the maximum height of the basketball?
y(in this case h) of the vertex. So
[tex]\Delta = b^2-4ac = 10^2 - 4(-4)(18) = 388[/tex]
[tex]y_{v} = -\frac{388}{4(-4)} = 24.25[/tex]
The maximum height of the basketball is of 24.25 feet.
Answer to the question?
Answer:
35
Step-by-step explanation:
AEC and AEB form a straight angle(180°)
180-40=140
AEV and AED are equal
140 divided by 4 = 35
Is segment ST tangent to circle P1
Answer:
B . Yes
Step-by-step explanation:
Recall: a tangent of a circle is perpendicular to the radius of a circle, forming a right angle at the point of tangency.
Therefore, if segment ST is tangent to circle P, it means that m<T = 90°, and ∆PST is a right triangle.
To know if ∆PST is a right triangle, the side lengths should satisfy the Pythagorean triple rule, which is:
c² = a² + b², where,
c = longest side (hypotenuse) = 37
a = 12
b = 35
Plug in the value
37² = 12² + 35²
1,369 = 1,369 (true)
Therefore we can conclude that ∆PST is a right triangle, this implies that m<T = 90°.
Thus, segment ST is a tangent to circle P.
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a blue marble is
7
8
.
There are 56 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answer:
7
Step-by-step explanation:
The probability of choosing a blue marble is 7/8, or 49/56, which means that out of 56 marbles, 49 are blue. 56-49=7, so there are 7 red marbles. Hope this helps! :)
Work out the lengths of sides a and b.
Give your answers to 1 decimal place.
17 cm
a
a
b
8 cm
12 cm
5 cm
Answer:
No solution is possible since you failed to provide the necessary information
Step-by-step explanation:
PLEASE ANSWER!! Find EF using Pythagorean theorem. Express answer to one decimal place.
Answer:
115.5 cm
Step-by-step explanation:
A^2 + B^2 = C^2
41^2 + 108^2 = C^2
C^2 = 13345
C = 115.5 cm
please help now
Your pump empties the water from a swimming pool in 4 hours. When your friend's pump is used together with your pump, the pool is emptied in 48 minutes. How long (in hours) does it take your friend's pump to empty the pool when working alone?
Answer:
Time taken for pump B to empty pool = 1 hour.
Step-by-step explanation:
Given:
Time taken for pump A to empty pool = 4 hour
Time taken together = 48 minutes = 48 / 60 = 4/5 hour
Find:
Time taken for pump B to empty pool
Computation:
Assume;
Time taken for pump B to empty pool = a
1/4 + 1/a = 1 / (4/5)
1/4 + 1/a = 5/4
1/a = 5/4 - 1/4
1/a = (5 - 1) / 4
1/a = 1
a = 1
Time taken for pump B to empty pool = 1 hour.
Question 14 of 14
Which expression gives the distance between the points
(1,-2) and (2, 4)?
O A. (1+23° +(2-47
O B. (1-2)*+(-2-4)
O c. 111-23 +4:32-47
O D. Hit+2y +(2-479
Answer:
c
Step-by-step explanation:
Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables.
Michael
Lemons
Cups of Water
1 4
3 12
4 16
Sondra
Lemons
Cups of Water
2 6
4 12
6 18
Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?
Answer:
1/4= 3/12 & 2/6 = 4/12
Step-by-step explanation:
Answer:
Its simply B
Step-by-step explanation:
If we are to express both ratios in their simplest form, we will have the ratio of Michael’s lemonade is 1:4 and that of Sondra is 1:3. The denominator that can be used in order to compare the ratios is that which can be divided by both ratios. For example, we have 12 as a denominator. The ratios can be expressed as 3/12 and 4/12. Also, the denominator can be 24 such that the ratios can be expressed as 6/24 and 8/24.
Find the surface area of the regular pyramid.
Destiny has borrowed $8 from 7 different friends. Write an integer that
represents Destiny's total debt to her friends.
Answer:
56
Step-by-step explanation:
7×8=56
Hope this helps! :)
A ramp is in the shape of a triangle
Answer:
Step-by-step explanation:
The radius of a circle is 10 cm. Find its circumference in terms of \piπ.
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Radius of the circle "[tex]r[/tex]" = 10 cm.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The circumference of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:20\:π\:cm.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]
[tex] = 2 \: \pi \times 10 \: cm \\ \\ = 20 \: \pi \: cm[/tex]
Therefore, the circumference of the circle is 20 π cm.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
Which inequality is true?
А. Зп > 9
B. 7 + 8< 11
C. 27 -1 < 5
D. 2 > 2
SUBMIT
< PREVIOUS
9514 1404 393
Answer:
А. Зп > 9
Step-by-step explanation:
The inequality of A may or may not be true. (It is true only if n > 3.) All of the others are definitely false.
Kern Shipping Inc. has a requirement that all packages must be such that the combined length plus the girth (the perimeter of the cross section) cannot exceed 99 inches. Your goal is to find the package of maximum volume that can be sent by Kern Shipping. Assume that the base is a square.
a. Write the restriction and objective formulas in terms of x and y. Clearly label each.
b. Use the two formulas from part (a) to write volume as a function of x, V(x). Show all steps.
Answer:
Step-by-step explanation:
From the given information:
a)
Assuming the shape of the base is square,
suppose the base of each side = x
Then the perimeter of the base of the square = 4x
Suppose the length of the package from the base = y; &
the height is also = x
Now, the restriction formula can be computed as:
y + 4x ≤ 99
The objective function:
i.e maximize volume V = l × b × h
V = (y)*(x)*(x)
V = x²y
b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):
y + 4x ≤ 99 --- (1)
V = x²y --- (2)
From equation (1),
y ≤ 99 - 4x
replace the value of y into (2)
V ≤ x² (99-4x)
V ≤ 99x² - 4x³
Maximum value V = 99x² - 4x³
At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]
[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]
⇒ 198x - 12x² = 0
[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]
By solving for x:
x = 0 or x = [tex]\dfrac{33}{2}[/tex]
Again:
V = 99x² - 4x³
[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]
At x = [tex]\dfrac{33}{2}[/tex]
[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]
[tex]\implies 198 - 12 \times 33[/tex]
= -198
Thus, at maximum value;
[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]
Recall y = 99 - 4x
when at maximum x = [tex]\dfrac{33}{2}[/tex]
[tex]y = 99 - 4(\dfrac{33}{2})[/tex]
y = 33
Finally; the volume V = x² y is;
[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]
[tex]V =272.25 \times 33[/tex]
V = 8984.25 inches³
Which expression entered into a graphing calculator will return the probability
that 35 or fewer heads come up when flipping a coin 100 times?
A. binomcdf(35, 100, 0.5)
B. binomcdf(100, 0.5, 35)
C. binomcdf(100, 35, 0.5)
O D. binomcdf(35, 0.5, 100)
Answer:
B. binomcdf(100, 0.5, 35)
Step-by-step explanation:
Binomcdf function:
The binomcdf function has the following syntax:
binomcdf(n,p,a)
In which n is the number of trials, p is the probability of a success in a trial and a is the number of sucesses.
35 or fewer heads come up when flipping a coin 100 times.
100 coins are flipped, which means that n = 100.
Equally as likely to be heads or tails, so p = 0.5
35 or fewer heads, so a = 35.
Then
binomcdf(n,p,a) = binomcdf(100,0.5,35)
The correct answer is given by option B.
In a sample of 400 students, 60% of them prefer eBooks.
A.Find 98% Confidence Interval for the proportion of all students that prefer ebooksb.
b. Find the margin of erro
Answer:
a) The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).
b) The margin of error is of 0.05.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In a sample of 400 students, 60% of them prefer eBooks.
This means that [tex]n = 400, \pi = 0.6[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.054[/tex].
Margin of error -> Question b:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 2.054\sqrt{0.6*0.4}{400}}[/tex]
[tex]M = 0.05[/tex]
The margin of error is of 0.05.
A.Find 98% Confidence Interval for the proportion of all students that prefer ebooksb.
Sample proportion plus/minus the margin of error.
0.6 - 0.05 = 0.55
0.6 + 0.05 = 0.65
The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).
If you apply the changes below to the reciprocal parent function, F(x) =
what is the equation of the new function?
• Horizontally stretch by multiplying by 1/6
• Translate 5 units right.
Answer:
The answer is "Option B".
Step-by-step explanation:
Please find the complete question in the attached file.
The Horizontal stretch [tex]=(\frac{1}{6 \ x})\\\\[/tex]
Translation by 5 units right[tex]=( \frac{1}{6\ x})-5[/tex]
Answer:
its A i used his answer and got it wrong
Could anyone help me please?
9514 1404 393
Answer:
4
Step-by-step explanation:
In order to evaluate f(g(-1)), you first need to find g(-1).
The graph of g(x) crosses the line x = -1 at y = 1, so g(-1) = 1.
The second step is evaluating f(1). The graph of f(x) crosses the line x=1 at y=4, so f(1) = 4.
f(g(-1)) = f(1) = 4
In 42 - 15 = 27, the number 42 is called the
the number 15 is called the
and the number 27 is called
Answer:
The Answer to the Ultimate Question of Life, the Universe, and Everything is 42
Step-by-step explanation:
In this equation, the number 42 is called a minuend.
15 is a subtrahend because it is being subtracted from another number.
The number 27 would be called the difference.
Drew hiked two trails Rocky Hill is 7 /8 miles long battle in Brook Trail is 4/5 mile long how much further did Drew hike on Rocky Hill Trail then I'll babbling Brook Trail write an equation
The retail cost of a TV is 50 % more than its wholesale cost. Therefore, the retail cost is ____ times the wholesale cost.
Answer:
Let the retail cost be x and the wholesale cost be y
Step-by-step explanation:
x = y + 0.50y
x = 1.50y
Therefore the retail cost is 1.50 times the wholesale cost.
. What is the solution of the system of equations 3x + 2y = 4 and -2x + 2y = 24? *
Answer:
x= -4
y= -8
This will be the solution
At Downunder Farms, Jamie is packing kiwi fruit in shipping crates. Each tray
holds 58 kiwis, and he can put 6 trays in a crate. How many kiwis does the
crate contain when it is full?
A. 64 kiwis
B. 290 kiwis
C. 348 kiwis
D. 174 kiwis
Answer:
348 kiwis
Step-by-step explanation:
Jamie is packing Kiwie fruits into a tray
Each tray holds 58 kiwis
He can put 6 trays in a crate
Hence when the craye is full the number of kiwis it will contain can be calculated as follows
°= 58×6
= 348 kiwis
Solve for z
3z-5+2z=25-5z
Answer:
z=3
Step-by-step explanation:
1. collect like terms
5z-5=25-5z
2. Move the variable to the left hand side and change its sign
5z-5+5z=25
3. Collect like terms
10z=25+5
4. Divide both sides of the equation by 10
z=3
The solution to the equation is z = 3.
To solve for z in the equation 3z - 5 + 2z = 25 - 5z, we can simplify and combine like terms on both sides:
3z + 2z + 5z = 25 + 5
Combining the terms on the left side gives:
10z = 30
Next, we isolate the variable z by dividing both sides of the equation by 10:
(10z)/10 = 30/10
This simplifies to:
z = 3
Therefore, the solution to the equation is z = 3.
To know more about equation:
https://brainly.com/question/10724260
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33. Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5
b. The constant is 2
C. The power is 10
d. The constant is 5
Answer:
Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5. ( true)
b. The constant is 2
C. The power is 10
d. The constant is 5
Two trains leave a train station at the same time. One travels north at 12 miles per hour. The other train travels south at 9 miles per hour. In
how many hours will the two trains be 88.2 miles apart?
O 4.7 hours
O 4.2 hours
O 2.1 hours
O 8.4 hours
Answer:
4.2 hours
Step-by-step explanation:
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $2000 loan for 48 months at 3.5% APR. How much total interest will you have paid at the end of the 48 months? (Round your answer to the nearest cent.)
$
Step-by-step explanation:
Are you using a particular calculator for the class? For this class, is the payment expected to be compounded monthly?
There is a function in Microsoft Excel that will calculate the payment for you, but the answer is going to be slightly different for a business math class than a calculus-based statistics class.
The excel formula to calculate a payment is
=PMT(0.04/12,60,25000,0)
.04/12 is the interest APR on a monthly basis
60 is the number of months
25000 is the current amount owed
0 is the future balance after 60 payments
The answer from Excel is $460.41 -- ignore the negative sign for these purposes.
Multiply that number by the 60 months you pay and you get a total paid of $27,624.78
Remove the initial 25K and $2,624.78 is your interest amount.
By the way, I used the simplifying assumptions that the problem meant "interest rate" when it said "APR", and that the rate would compound monthly. In the actual loan industry, the interest rate is only part of the calculation for APR, a
146.08
Step-by-step explanation:
Let's start by figuring out the payment
effective rate: .035/12= .002916667
\begin{gathered}2000=x\frac{1-(1+.002916667)^{-48}}{.002916667}\\x=44.71\end{gathered}
2000=x
.002916667
1−(1+.002916667)
−48
x=44.71
then it's just
44.71*48-2000=146.08
Answer:
146.08
Step-by-step explanation:
Let's start by figuring out the payment
effective rate: .035/12= .002916667
[tex]2000=x\frac{1-(1+.002916667)^{-48}}{.002916667}\\x=44.71[/tex]
then it's just
44.71*48-2000=146.08
I’ll give brainliest
OPTION A
y= 3x+6
This equation satisfies for all the value given in the table.
For (0,6)
y = 3(0)+6 = 6
For (2,12)
y=3(2) +6 = 6+6= 12
And so on.
Find the distance between a point (–7, –19) and a horizontal line at y = 3.
