The number of minutes it will take the marshal to catch up to the robber in discuss is; 210.
How long will it take to catch up with the robber?Let 30minutes = 0.5 hours.
Let x represent the time for which the marshal has ran.
On this note, the robber must have galloped at; (x +0.5) hours.
Hence, it follows from the task content that if they are at the same distance from the bank; we have;
14(x+0.5) = 16(x)
14x + 7 = 16x
7 = 2x
x = 7/2 = 3.5 hours.
= 3.5 × 60minutes = 210minutes.
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Three hundred fifty seniors attended
the spring prom. If this number repre-
sents of the total senior class, then
how many seniors are in the class?
7
Answer:
there would be three hundred and fifty.
-5+9-4-(-4)+(-9)-12+7
Answer:
Step-by-step explanation:
if you multiply a negative number with another negative number, it will be positive: ( - ) x ( - ) = ( + )
and if you multiply a negative number with a positive number, it will be negative: ( - ) x ( + ) = ( - )
so -(-4) = 4 and +(-9) = -9
-5+9-4+4-9-12+7=-10
I hope this helps
The width of a 2-by-4 piece of wood is actually 3 1/2 inches. Find the total width of 30 2-by-4s laid side by side. Simplify your answer.
This is equivalent to 8.75 feet
====================================================
Explanation:
3 & 1/2 inches = 3.5 inches since 1/2 = 0.5
30 boards of this width total to 30*3.5 = 105 inches
This is equivalent to 105/12 = 8.75 feet. I'll leave the answer in inches since the original unit is inches. I would ask your teacher for further clarification.
HELPP I WILL MSRK YOU BRAINLIST…
Answer:
< - 9, 11 >
Step-by-step explanation:
consider the end points of the vector
(5, - 2 ) and (- 4, 9 )
x- direction is then - 4 - 5 = - 9
y- direction is 9 - (- 2) = 9 + 2 = 11
then vector in component form is < - 9, 11 >
Sketch the solid that results when the region enclosed by the given equations is revolved about the x -axis.
y = x²
y = 0
x = 2
y = x², y = 0, x = 2 are region enclosed by the given equations is revolved about the x -axis.
What exactly is a closed area?
All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.
What do you mean by the region that a closed curve encloses?
The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.
Whether contained or not?
Use enclosed at all times. No longer regarded as a regular variety, enclosed would even be mistaken for another word by many readers. Use enclose, encloses, and enclosing rather than in close for other words that are similar to enclosed.Learn more about enclosed region
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How to solve? I tried but I found no answers.
Answer:
x=1
Step-by-step explanation:
Perimeter of the square is 4 times the side = 4*(4x-1)
Perimeter of Rectangle = 2 L + 2 W = 2*(2x+2) + 2*2x
4*(4x-1) = 2*(2x+2) +4x
16x-4= 4x+4+4x
16x-4 = 8x+4
16x-8x = 4+4
8x = 8
x = 8/8
x=1
Hope this helps!^^
Find the coordinates of the orthocenter of each triangle with the given vertices. R(-4,8), S(-1,5), T(5,5)
The orthocenter is the point where a triangle's three altitudes intersect, and the centroid is the point where the three medians intersect.
The coordinates of the orthocenter of Δ RST is (–4, –4).
What is the orthocenter of the triangle?
An orthocenter of a triangle is the point at which altitudes drawn perpendicular from the vertex to the opposite sides of a triangle intersect. A triangle typically has three altitudes, and the intersection of all three altitudes is known as the orthocenter.
The orthocenter is the point where a triangle's three altitudes intersect, and the centroid is the point where the three medians intersect.
The slope of RS is (5-8)/(-1+4) or –1. So, the slope of the altitude, which is perpendicular to RS is 1.
Now, the equation of the altitude from T to RS is:
y - 5 = 1(x - 5)
y = x
Use the same way to find the equation of the altitude from R to ST. That is,
Y - 8 = -1/0 (X + 4 ) or x = -4
x = -4 and y = -4
Solve the equations to find the intersection point of the altitudes. So, the coordinates of the orthocenter of Δ RST is (–4, –4).
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James had $72 in his bank account. he bought a $75 painting from my local artist and paid with a check. he thought the artist will take a few days to deposit the check. he knows he will have enough money to cover the amount of the check once his paycheck is deposited, but he received a text notification the next day that his account balance was -$45. how much was james charge for an overdraft fee? make a claim. include textual evidence. show reasoning.
James was charged $42 for an overdraft fee for the purchase of the painting.
James had $72 in his bank, paying for a painting worth $75 with a cheque meant he had extra $3 for him to balance the local artist. Receiving an account balance was -$45 meant the bank helped James cover the extra $3 he was owing while charging him additional $42 for overdraft on the account. In mathematical relation, it is described as;
Cash in bank – cost of painting = ($72- $75)
= -$3
Thus, overdraft is calculated as;
Overdraft=Balance + amount to balance cost of painting = (-$45) + $3
=-$42
Therefore, James was charged an overdraft of $42 for the purchase of the painting.
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10 Points
Use the figure below to answer questions #1-4. You can also use DESMOS to help you answer this question.
What are the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE
Using translation concepts, the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE are given by: (3,4).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
The rule for a 90º clockwise rotation is given by:
(x,y) -> (y, -x).
From the figure given for the problem, the coordinates of G are given as follows:
G(-4,3).
Applying the rule, we have that:
(-4,3) -> (3, 4), as y = 3, -x = -(-4) = 4.
Hence the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE are given by: (3,4).
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Sarah was explaining her first step in factoring, but made an error in her explanation.
Factor: 5x² - 4x - 9
Sarah said, "I need to find factors of -9 that add to -4"
What was the error in her thought process?
Answer:
-9
Step-by-step explanation:
her error was that -9 can't add up to -4
Answer:
she needs to find factors of -45 that add to -4
Step-by-step explanation:
You want to know the error involved when looking for factors of 5x²-4x-9 by considering only factors of -9.
Quadratic factorsConsider the product of factors (ax +b)(x +d):
(ax+b)(x +d) = ax² +adx +bx +bd = ax² +(ad+b)x +bd
You will notice the two parts of the sum that is the middle term coefficient have the product abd, which is also the product of the first and last coefficients.
Sarah needs to be looking for factors of (5)(-9) = -45 that have a sum of -4.
__
Additional comment
The factors Sarah needs are -9 and 5. These will give Sarah the equation ...
5x² -9x +5x -9
which can be factored pairwise to ...
x(5x -9) +1(5x -9) = (x +1)(5x -9)
Some people think that the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, resembles a golf ball. The building is a sphere measuring 165 feet in diameter. A typical golf ball has a diameter of approximately 1.5 inches.
a. Find the volume of Spaceship Earth to the nearest cubic foot.
The Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, a sphere building measuring 165 feet in diameter, has a volume of 2,352,071 cubic feet.
Volume refers to the amount of space occupied by a three-dimensional object.
Based on the problem, the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida is a sphere building measuring 165 feet in diameter. If radius is half of the diameter, then it has a radius of 82.5 feet.
The volume of the Spaceship Earth geosphere can be calculated using the formula for the volume of a sphere given by:
V = 4/3 π r^3
V = 4/3 π (82.5 feet)^3
V = 4/3 π (561,5151.625 cubic feet)
V = 2,352,071.15 cubic feet
Rounding off to the nearest cubic foot,
V = 2,352,071 cubic feet
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Convert 55°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C = (F-32)
9
F-C+32
=
Answer:
search up
Step-by-step explanation:
A
You are given two metal cubes that look similar. One has an edge of 3. 2 cm long and a mass of 43. 63 g. The other has an edge of 8. 34 cm long and a mass of 683. 5 g. How can you determine if both cubes are made from the same material? select the true statements.
By solving for the density of the two metal cubes, we can determine that the two metal cubes are not made from the same material.
Density, denoted by ρ, is a property of any substance that is defined as the ratio between the mass and volume of the substance.
ρ = m/v
where ρ = density
m = mass
v = volume
Solving the density of each cube.
Cube 1 :
ρ = m/v
ρ = m/e^3
ρ = 43. 63 g/(3. 2 cm)^3
ρ = 1.3315 g/cm^3
Cube 2 :
ρ = m/v
ρ = m/e^3
ρ = 683. 5 g/(8. 34 cm)^3
ρ = 1.1783 g/cm^3
If two objects have the same density, then they are made from the same material. Since the density of the two cubes are not equal, then they are not made form the same material.
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A stereo player is pricer at $1320 plus value added tax at 15% how much does the stereo player actually cost
Answer:
$1518
Step-by-step explanation:
Take the 1320 and multiply it by 0.15 (15% as a decimal) to get 198
Then add the 198 to the 1320 to get 1518
In an examination 50 candidates sat for either Mathematics or English language 60% passed in Mathematics and 48% passed in English language. If each candidate passed in at least one of the subjects, how many candidates passed in (i) Mathematics (Ii) English language. Illustrate the information above in a Venn diagram. Use the Venn diagram to find the number of candidates who passed both subjects
A Venn diagram can be used to solve it.
Candidates passed in mathematics = 26Candidates passed in English = 20A Venn diagram is what?A Venn diagram is a type of diagram where the relationships between items or groups of objects are represented by circles. While circles that do not overlap do not share any features, overlapping circles do. Venn diagrams are used to illustrate the parallels and differences between two concepts visually.
The Venn figure shows that 4 students passed both courses and that 20 students succeeded in English while 26 students passed in mathematics.
P(A∪B) = P(A) + P(B) - P(A∩B)
50 = 30 + 24 - (candidates who passed both subjects)
(candidates who passed both subjects) = 4
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Determine whether the events are independent or dependent. Then find the probability.
A king is drawn, without replacement, from a standard deck of 52 cards. Then, a second king is drawn.
1/13 is probability of a second king is drawn.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective.Total cards = 52
a complete pack without jokers, then it is 4/52 = 1/13.
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Write an equation of each line in standard form with integer coefficients.
the line through (-4,6) and (2,-2)
The equation of the line in standard form passing through the points (-4 , 6) and (2 , -2) is 4x + 3y = 2.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.
Given two points, (-4 , 6) and (2 , -2), use the two-point form to generate the equation of the line.
y - y2 = [(y2 - y1)/(x2 - x1)] (x - x2)
y - -2 = [(-2 - 6)/(2 - -4)](x - 2)
y + 2 = (-8/6)(x - 2)
y + 2 = -4/3 x + 8/3
To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
y + 2 = -4/3 x + 8/3
4/3 x + y = 8/3 - 2
4/3 x + y = 2/3
Multiply both sides by 3 to have integer coefficients.
3(4/3 x + y) = 3(2/3)
4x + 3y = 2
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Question 2 of 10
What is the third quartile of the following data set?
20, 21, 24, 25, 28, 29, 35, 37, 42, 43, 44
OA. 37
OB. 42
OC. 35
OD. 29
The third quartile of the given data set is 42.
What is third quartile?The third quartile (Q3, or the upper quartile) is the 75th percentile, meaning that 75% of the data falls below the third quartile.
Given is a data set, 20, 21, 24, 25, 28, 29, 35, 37, 42, 43, 44 we need to find the third quartile of the data set,
To find the third quartile we will use the given below formula,
Q3 = 3/4 (n+1)th term,
n = 11
Q3 = 3/4 (11+1)
Q3 = 3/4 x 12
Q3 = 9th term
= 42
Hence, the third quartile of the given data set is 42.
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What are the multiplication facts for 5? pls help marking brainly
Answer:
it is as follows:
5x2=10
5x3=15
5x4=20
5x5=25
5x6=30
5x7=35
5x8=40
5x9=45
Step-by-step explanation:
Answer: 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150
Step-by-step explanation:
16-19!!! NEED NOW!!!
Answer:
(15 solutions)[tex]2x + 9 = y \\ - 4x - 3 = y \\ so \: both \: equation \: is \: equal \\ 2x + 9 = - 4x - 3 \\ 2x + 4x = - 3 - 9 \\ 6x = - 12 \\ x = \frac{ - 12}{6} \\ x = - 2[/tex]
if this solution is correct then I'll solve another..... please reply my solution is correct or wrongwhat is 50 times 4
giving away points
Answer: 200
Step-by-step explanation: hope this helps!!!
hey don't ask it in this way
ask a easy real question
so mods won't take it down
thanks btw <3
On which interval does h(t) have an average rate of change of zero?
Answer:
In the interval (-∞, -5)
Step-by-step explanation:
Average rate of change of any graph is represented by the slope of the function in the given interval.
Rate of change =
= change in the y-coordinates
= change in the x-coordinates
If = 0, then the rate of change will be zero in that interval
From the graph attached,
From x = -∞ to x = -5, we find a flat line, showing
Therefore, average rate of change of h(x) in the interval (-∞, -5) is zero
You are solving a measurement problem where the numbers 4.5160 x 10−3, 2.09 x 107, and 5.8 x 103 are multiplied. how many significant digits should the product have? 2 1 5 3
The number of significant digits the product should have = 2
The given numbers are:
[tex]4.5160 \times 10^{-3}\\ 2.09 \times 10^7\\ 5.8 \times 10^3[/tex]
We first multiply them.
[tex]4.5160 \times 10^{-3}\times 2.09 \times 10^7\times 5.8 \times 10^3 = 54.743\times10^7[/tex]
In measurement problems, we usually write it as [tex]5.474\times10^7[/tex]
Significant digits are the numbers which decide the precision and accuracy in measurement problems.
The fewest number of significant digits in each factor of multiplication is considered as the significant digits of the product.
So number of significant digits in [tex]4.5160\times10^{-3}[/tex] = 5
Number significant digits in [tex]2.09\times10^7[/tex] = 3
Number of significant digits in [tex]5.8\times10^3[/tex] = 2
So the product should be rounded into 2 significant digits.
So the product, [tex]5.474\times10^7[/tex]= [tex]5.5\times10^7[/tex] with 2 significant figures.
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The man in the video spent 9 minutes and 2 seconds to fill his bathtub before taking a bath. After taking the bath, his partner told him that taking a bath was wasting water, and he should shower instead.
Question: How long would he need to run the shower to use the same amount of water as the bath that he took?
Please respond in one clear, succinct paragraph. Be sure to clearly state your final answer and include all of your mathematical reasoning that led you to your final answer. You will be graded on how accurate your final answer is and how clearly you were able to explain your answer. Make sure you write in complete sentences with proper writing conventions (i.e. grammar, punctuation, spelling).
Answer:
he will take the same time as its the same flow of water so he will spend 9 min and 2 sec
How much more would $10,000 earn in 3 years compounded daily at 1.33%, than compounded semi-annually at 4.33%? Round to the nearest cent. Please include the formulas used :)
The difference between $10,000 invested at 1.33% compounded daily and 4.33% compounded semi annually is $11,188.99.
What is the difference?When an amount earns interest that is compounded daily, it means that both the amount invested and the interest accrued increases in value every day over the 3 year period.
If an interest is compounded semi-annually, it means that both the amount invested and the interest accrued increases in value two times in a year.
The formula that can be used to determine the future value when the amount is compounded is:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of years10,000 x [1.133^(3 x 365) ] - [1.0433^(2x3)]
10,000 x (2.4085 - 1.29)
10,000 x 1.119 = $11,188.99
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Identify a pattern and find the next three terms in the pattern.
-4,-3,-2,-1, . . .
Pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2
As given,
Given pattern is -4,-3,-2,-1, . . .
a₁ =-4
a₂ =-3
a₃ =-2 ….
d =a₂ - a₁
=-3 - (-4)
=1
Pattern is arithmetic progression with d=1.
aₙ =a₁ + (n-1)d
a₅ =a₁ + (5-1)d
=-4 +4(1)
=0
a₆ =-4 + 5(1)
=1
a₇ =-4 +6(1)
=2
Therefore, pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2
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.
Will the product of an integer and a natural number always be an integer? Why or why not? Justify your answer with two examples.
Yes, the product of an integer and a natural number will always be an integer.
A natural number refers to a whole number that does not have any kind of fraction or decimal. Some examples of natural numbers are 1, 2, 3, 4, and so on. Zero is not a natural number.
Integers refer to all numbers that can be positive and negative. It should not have a fractional part or a decimal part in the number. Integers can be depicted by the positive or the negative sign. Zero is an integer.
Whenever we are multiplying a natural number with an integer, we are ultimately getting the result as a positive number, negative number, or zero. Thus, it will become an integer.
Example 1: We can take the natural number 10 and the integer -5. Its product will be -50. Thus, it is an integer.
Example 2: We can take the natural number 16 and the integer 0. Its product will be 0. Thus, it is an integer.
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The art club raised $248 through fundraisers. then they spent $206 to set up an art show. they raised another $316 at the art show. how much money did the art club have after the show?
Using basic mathematical operations such as addition and subtraction, the art club have $358 after the show.
Basic mathematical operations includes addition, subtraction, multiplication, and division.
Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.
If the art club raised $248 through fundraisers, spent $206 to set up an art show, and raised another $316 at the art show, adding the total amount they raised and subtracting the amount they have spent, we can solve how much money they have after the show.
$248 - $206 + $316 = $358
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two numbers to multiply to get -120
Answer:
-60 x 2= -120
Step-by-step explanation:
Answer:
-40 * 3
Step-by-step explanation:
Just one example of many
If f(x) = sqrt(4 - x ^ 2) then f(2)
Answer:
f(2) = sqrt(4 - 2 ^ 2)
f(2) = sqrt(4 - 4)
f(2) = sqrt(0)
f(2) = 0
Answer: 0
Step-by-step explanation:
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