Answer:
16,400 ft
Step-by-step explanation:
You want to know the number of feet in a 5 km race, rounded to the nearest hundred. You are given conversion factors 5280 ft = 1 mi = 1.61 km.
Unit conversionUnit conversion can be done by multiplying by a conversion factor whose numerator is equal to its denominator, and that cancels unwanted units, replacing them with units you want.
[tex]5\text{ km}=5\text{ km}\times\dfrac{5280\text{ ft}}{1.61\text{ km}}\approx16397.5\text{ ft}\approx\boxed{16,\!400\text{ ft}}[/tex]
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Additional comment
Both of the given conversions are equal to 1 mile, so their ratio is 1. We put feet on top of the fraction, because that is the unit we want. The km value is in the denominator so the km units in numerator and denominator cancel.
The conversion for km is 1 mi = 1.609344 km (exactly). The actual conversion to ft will give 16,404 76/381 ft. This has a very long repeating decimal fraction.
The Smith and Jones manufacturing company keeps a third of its cash in the bank, which pays 0.5% interest, and the other two-thirds in long-term investments that give 3.5% interest. If the company earned a total of $37,500 in interest last year, how much cash did they keep in the bank?
If the company earned a total of $37,500 in interest last year, how much cash did they keep in the bank is; $937,500.
How to solve Algebra Word Problems?This is about the concept of compound interest which is defined as the interest on savings that is calculated on both the initial principal and the accumulated interest from previous periods.
From the question, let us make x to represent the amount of cash.
Now, we are told that one portion of it pays 0.5%and as such this will be 0.005x.
Now, the other portion pays 3.5% and as such this is 0.035x.
Combining both knowing that the total the company earned in the last year was $37,500 and we have;
0.005x + 0.035x = 37500
0.040x = 37500
Solve for x to get;
x = (37500)/(0.04)
x = 937500
Therefore, the company started with $937,500.
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I need help please !!!
Answer: can you guys help me too
Step-by-step explanation:
Together, Nora and Addison own 152 shares of stock. Nora has 4 less than three times Addison's amount. How many shares does each girl have?
Set both given equations equal to zero, then combine them into one standard form equation. Simplify if possible.
7x + 3 = 5 and y - 1 = 6
Equation 1 -
Equation 2 -
Combined Equation -
Answers:
a. 7x - 2 = 0
b. 7x - y = 1
c. 7x + 8 = 0
d. y - 7 = 0
e. 7x - y = -5
f. y + 7 = 0
The standard equation is 7x + y = 9
layoff Ax + By = C is the usual form for two-variable direct equations. A standard form direct equation is, for case, 2x + 3y = 5. When an equation is given in this format, chancing both intercepts is rather simple( x and y). When trying to break systems involving two direct equations, this form is also relatively helpful.
Given
7x + 3 = 5 and y - 1 = 6
Add the bottoms from the two given equations to produce a single standard-form equation.
By shifting the constant fromR.H.S. toL.H.S., the equations are reset to zero.
7x + 3 - 5 = 0
7x - 2 = 0----( 1)
y - 1 = 6
y - 1 - 6 = 0
y - 7 = 0-----( 2)
Equation 1 and equation 2 must be combined.
7x - 2 + y - 7 = 0
7x + y - 9 = 0
layoff Ax + By = C is the equation's conventional form.
A, B, and C are integers and x and y are variables in this type of equation.
Accordingly, the common equation is
7x + y - 9 = 0
7x + y = 9
therefore the standard equation is 7x + y = 9
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Factor x^2 -2x -2. Show all steps
Answer:
x = 1 ± √3
Step-by-step explanation:
Factorizing using quadratic formula:x² - 2x - 2
Co-efficient of x² = a = 1
Co-efficient of x = b = -2
Constant = c = -2
D = b² - 4ac
= (-2)² - 4 *1*(-2)
= 4 + 8
= 12
[tex]\sf x = \dfrac{-b \ \± \sqrt{D}}{2a}[/tex]
[tex]\sf = \dfrac{2 \ \± \sqrt{12}}{2*1}\\\\\\=\dfrac{2 \± \sqrt{2*2*3}}{2}\\\\\\= \dfrac{2 \±2\sqrt{3}}{2}\\\\\\= \dfrac{2}{2} \± \dfrac{2\sqrt{3}}{2}\\\\\\= 1 \± \sqrt{3}[/tex]
[tex]\sf x = 1 + \sqrt{3} ; \ ; or \ x = 1 - \sqrt{3}[/tex]
The enrollment for a school in 2010 was 1245 students. in 2020, the enrollment was 715 students. find and interpret the rate of change in enrollment from 2010 to 2020
The rate of change in enrollment from 2010 to 2020 is -53 students per year.
Interpretation:
A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.
Here, we have,
To find the rate of change in enrollment from 2010 to 2020, we can use the formula for calculating the rate of change:
Rate of change = (Change in enrollment) / (Time interval)
Where:
Change in enrollment = Enrollment in 2020 - Enrollment in 2010
Time interval = Year in 2020 - Year in 2010
Let's calculate the rate of change:
Change in enrollment = 715 - 1245 = -530
Time interval = 2020 - 2010 = 10 years
Rate of change = (-530) / 10 = -53
The rate of change in enrollment from 2010 to 2020 is -53 students per year.
Interpretation:
A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
74°
(8x-19)°
45°
Answer:
x = 10
Step-by-step explanation:
The internal angles of a triangle sum 180°
74° + 45°+ (8x-19)° = 180°
119 + 8x - 19 = 180
119 - 19 + 8x = 180
100 + 8x = 180
8x = 180 - 100
8x = 80
x = 80/8
x = 10
Check:
74 + 45 + (8x-19) = 180
1100 + 8*10 = 180
100 + 80 = 180
What is the remainder of (x3+5x2−32x−7)÷(x−4) ? Enter your answer in the box.
Show all work please!
The remainder of the given division ( x³+5x²−32x−7 ) ÷ ( x−4 ) is equal to 9.
As given in the question,
Dividend of the given division is equal to : ( x³+5x²−32x−7 )
Divisor of the given division is equal to : ( x−4 )
Divide the given dividend ( x³+5x²−32x−7 ) by divisor ( x−4 ) remainder we get,
( x³+5x²−32x−7 )
= x³ -4x² +9x² -36x +4x-16 +9
= x²(x-4) + 9x (x-4) +4(x-4) + 9
= (x-4)(x² +9x +4) + 9
Quotient is equal to (x² +9x +4)
Remainder is equal to 9
Therefore, the remainder of the given division ( x³+5x²−32x−7 ) ÷ ( x−4 ) is equal to 9.
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help help help help help
Answer:
1 4/10
Step-by-step explanation:
3 1/2 turns into 3 5/10 minus 4 9/10 blah blah blah anyways yeah
Which relation represents a function?
The relation that represents a function is the mapping in: B.
How to Determine if a Relation is a Function?A relation is defined as a function if each of the x-value (domain element of input) in the relation corresponds to exactly one y-value (range element of output).
The relation in option A is not a function because it has two different y-values, 7 and 5 that corresponds to an x-value, 6. The relations in option C and D do not represent a function also.
The mapping in option B shows a relation where each x-value (domain element) is related or corresponds to only one y-value (range element). Therefore, it is a function.
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In angle L M N the measure of angle L is equal to the measure of angle M. The measure of angle N is twice the measure of angle M. Find the measure of each angle in angle L M N
The measure of ∠M and ∠L is 45 degrees. then the measure of ∠N is 90 degrees.
How does an angle form?An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints. The point of their joint is called vertex of that angle. Those two line segments forming it are called arms of that angle. The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.
Given that the angle L M N the measure of angle L is equal to the measure of angle M.
∠L = ∠M
Also, the measure of angle N is twice the measure of angle M.
∠N = 2∠M
The measure of each angle in angle L M N would be;
∠L + ∠M + ∠N = 180
∠M + ∠M + 2∠M = 180
4∠M = 180
∠M = 180/4
∠M = 45
∠M = ∠L = 45 degrees
∠N = 2 x 45 = 90
Therefore, the measure of ∠M and ∠L is 45 degrees. then the measure of ∠N is 90 degrees.
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What’s x??
Solve for X
5x-9=3x+3
Answer:
x = 6
Step-by-step explanation:
5x - 9 = 3x + 3 ( subtract 3x from both sides )
2x - 9 = 3 ( add 9 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6
i need this answer cause I have no clue what I'm supposed to do
The missing co-ordinate r = 8
(6,9) and (r,-1) are two points on a line whose slope is given as -5.
Slope of a line is the change of y co-ordinates divided by the change in x co-ordinates between two points on a line.
Take (x₁, y₁) = (6,9) and (x₂, y₂) = (r, -1).
The slope of a line is given by,
Slope, m = (y₂-y₁)/ (x₂-x₁)
⇒ -5 = (-1-9)/(r-6)
⇒ -5 = -10/(r-6)
⇒ 1 = 2/(r-6)
⇒ r-6 = 2
⇒ r = 2+6
⇒ r = 8
So the points are (6,9) and (8,-1).
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A parachutist descends 70 feet in 5 seconds. What integer represents the parachutist's change in height in feet per
second?
An integer is any number that contains both positive and negative numbers, including zero. The change in elevation exists 14 feet per second.
What is meant by an integer?An integer is any number that contains both positive and negative numbers, including zero. It does not contain fractional or decimal parts.
Integers include zero, a positive natural number, and a negative integer represented by a minus sign. The negative numbers are the inverse additions of the comparable positive numbers.
A parachutist descends 70 feet in 5 seconds.
To find this simply divide the numbers as shown: 70 feet in 5 seconds
70 / 5 = 14 seconds
Therefore, the change in elevation exists 14 feet per second.
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the distance between (2, -3) and (4, -3) on the coordinate plane?
[tex]=\sqrt{(x_{2} -x_{1})^{2}+(y_{2}-y_{1} )^{2} }\\ =\sqrt{(4-2)^{2}+(-3-(-3))^{2} } \\=\sqrt{(2)^{2}+(-3+3)^{2} } \\=\sqrt{4+0^{2} } \\=\sqrt{4} \\=2[/tex]
the distance is equal to 2
I also provided you with the formula for future use.
The graph models the linear relationship between the distance traveled and the amount of time it took to get there. What is the rate of change of the distance traveled with respect to time?
A) 1/4
B) 4
C) 1/5
D) 5
Answer:
D) 5
Step-by-step explanation:
we see that every 4 hours 20 miles are traveled.
so, the rate of change of miles travels over hours is
20/4 = 5/1 = 5
in other words, the speed was 5 mph.
Mathematics Diagnostic Assessment
Maria wants to add to her CD collection. If a CD costs $8, which expression shows the cost of d CDs?
OA. 8 + d
OB. 8-d
OC. 8-d
OD. 8x d
True or False
1. 28<0
2. 126<0
3. 688<0
Answer:
1. False, 2. False, 3. False
Step-by-step explanation:
Find the values of x in this equation. 10 + |2x − 12| − 14 = 0
ken makes trail mix. the ratio of nuts to raisins is 3 to 5 . find the amount of nuts used in a trail mix that had ten cups of raisins
answer: 3 to 5 = 6 to 10 = 9 to 15
so the answer would be 6 raisins
Answer:
3x+4x=10x=10/7=1.42
Step-by-step explanation:
3x+4x=10x
7x=10x
10/7=
1.42
Margaret walks in 28 days if she walks for 30 minutes per day how long will she in 28 days?
Answer:
840 minutes or 14 hours
Step-by-step explanation:
30 min x 28 days = 840 min
:]
Answer: 14 Hours or 840 mins
30 × 28 = 840 mins = 14 hours
Is there anything like prodigy for high school students? i used to love laying prodigy but once I entered high school I couldn't because it wasn't in my level. so I would like to find something like prodigy for high school students or something where you can like walk around and do things instead of just doing boring flash cards for school.
Answer:
I don't think so, but maybe Prodigy has a game level for high schoolers. You could try searching Gooogle for it, but other than that, I don't think Prodigy does high school math games.
Step-by-step explanation:
Answer: So just ask them
Step-by-step explanation:
So like first tell your teachers and say "hey there mother clunker. Can we play prodigy?". and if they say "Nah fam we're in high school not trashy middle school or elementary school.". You say "SHUT YO PASTEY BUTT UP IM THE ALPHA MALE AND YOU SHOULD RESPECT ME. NOW TELL ME. CAN I PLAY PRODIGY?". If you do say that the teacher will always say "yes yes pls don't hurt me." then you get to play prodigy. Thank me.
F(x)= 2|x-5|+7 write a function reflection of x-axis
Answer: -2Ix-5I - 7
Step-by-step explanation:
all you need to do is Multiply the entire equation by -1
The drive from Tallahassee Florida to Tampa takes about 5 1/2 hours while driving the posted speed limit the drive to from Tampa to fort Myers fla take 1 1/2 hours driving the posted sped limit. If you left Tallahassee at 2:30 am and drove directly to Tampa and then directly to fort myers fla, at the posted speed limit what time would you arrive at fort Myers fla
You will arrive at Myers fla by 9:30 am
an atleate can swim 1/2 mile every 1/ hour what is the unit rate
Answer:
3/2
Step-by-step explanation:
M is the midpoint of CF for the points C(4, 10) and F(10, 10). Find MF.
The length of the segment MF will be 6 units.
What is coordinate geometry?
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that M is the midpoint of CF for the points c(4,10) and f(10,10). To calculate the segment MF first let us calculate the midpoint M.
M = [ ( x₁ + x₂ ) / 2, ( y₁ + y₂ ) / 2 ]
M = [( 4 + 10 ) /2 , ( 10+10 ) / 2]
M = ( 7, 10)
The length of the segment MF will be:-
D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]
D = √ [ ( 10-10 )² + ( 10 - 4 )² ]
D = √36
D = 6
Therefore, the length of the segment MF will be 6 units.
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Charis invested 140$ . She earned a simple interest of 3%per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
The amount of interest would be $8.4 Charis received at the end of two years.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as:
Principal (P) = $140
Rate of Interest (R) = 3% = 3/100 = 0.03
Time (T) = 2 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
⇒ Simple interest = 140 × 0.03 × 2
⇒ Simple interest = $8.4
Therefore, the amount of interest would be $8.4 Charis received at the end of two years.
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help
D’Neese said that 1/10^5 is equivalent to 10^5 . Which statement is true about what D’Neese said?
D’Neese is correct because a^-n =1/a^n
D’Neese is correct because a^-n = 1//a^-n
D’Neese is incorrect because a^-n = -1/a^n
D’Neese is incorrect because a^-n = a/-n
The statement that is true about what D’Neese said is (d) D’Neese is incorrect because a^-n = a/-n
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the true statement about the equation statement ?The equation statement is given as
1/10^5 is equivalent to 10^5
The above statement can be rewritten in another way
So, we have the following equation
1/10^5 = 10^5
As a general rule of indices, we have the following exponent rule
So, we have the following equation
1/a^n = a^-n
This means that the equation statement is false
This is so because
1/10^5 is not equivalent to 10^5, instead 1/10^5 is equivalent to 10^-5
Hence, the true option about the statement is (d)
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Please help!!! I need an answer quick
is wine sir jacque the a beauty for the universe and
what does p equal [tex]\frac{p}{4} - -15 = 19[/tex]
The value of p from the given equation is 136.
The given equation is p/4 - 15 = 19.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is solved as follows:
Transpose -15 to other side of the given equation
That is, p/4 = 19+15
⇒ p/4 = 34
Cross multiply 4 to 34
We get p = 34 × 4
⇒ p = 136
Therefore, the value of p from the given equation is 136.
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what is −k−(−8k)? Im so confused i need desperate help!!!
Answer:
Step-by-step explanation:
-k-(-8k)
When there are 2 negatives, it becomes a plus. So, -(-8k) would become
+(8k).
So, -k-(-8k):
-k+8k Open parentheses and then subtract because there is a negative.
7k Answer.
I hope this clears things up a little!