The Reeds are moving across the country. Mr. Reed leaves 4.5 hours before Mrs. Reed. If he averages 40mph and she averages 60mph, how many hours will it take Mrs. Reed to catch up to Mr. Reed?
Answers
Answer:
Mr. Reed DATA:
rate = 40 mph ; time = x hrs ; distance = 40x miles
-----
Mrs. Reed DATA:
rate = 60 mph ; time = x - 3.5 hrs ; distance = 60x - 210 miles
Equation:
40x = 60x -210
-20x = -210
x = 10.5 hrs
x-3.5 = 7 hrs (Mr. Reed's time)
Step-by-step explanation:
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Related Questions
Find the value of x. If necessary round to the nearest tenth.
Answers
The value of x which is the dimension of the eternal part of the secant segment is 4.
What is the numerical value of x?The secant-tangent power theorem states that "if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment".
It is expressed as:
( tangent segment )² = External part of the secant segment × Secant segment.
From the diagram:
tangent segment = 6
External part of the secant segment = x
Secant segment = ( 5 + x )
Plug the given values into the above formula and solve for x.
( tangent segment )² = External part of the secant segment × Secant segment.
( 6 )² = x × ( x + 5 )
36 = x² + 5x
x² + 5x - 36 = 0
Using AC method:
( x - 4 )( x + 9 ) = 0
( x - 4 ) = 0 or ( x + 9 ) = 0
x = 4 or x = -9
Since we are dealing with dimensions, we take the positive value.
Hence:
x = 4
Therefore, the value of x is 4.
Option D) 4 is the correct answer.
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Billy took 5 tests in his math class. He scored an 89,88,93,90 and 81. What is the variance of his grades in these test? If necessary, round to the nearest hundredth.
Answers
The variance of Billy's grades obtained from his test scores is 15.76
What is variance?The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.
The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;
The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2
The square of the differences of the values from the mean can be calculated as follows;
(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84
The sum of the square of the differences is therefore;
0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8
The variance is therefore; 78.8/5 = 15.76Learn more on the variance of a set of data here: https://brainly.com/question/30701163
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what is the value of 7 in the number 21,780
Answers
Answer:
It us in the hundreds place . Hope that helps !
8. The first three terms of a geometric sequence are ( x-6), 3x, and y. If the common ratio is 6, then the value of y is.
Answers
Answer:
The value of y is 216
(and the value of x is 12)
Step-by-step explanation:
The general formula for a geometric sequence is,
\(a_n = a_1(r)^{n-1}\)
Where n represents the nth term, a_1 is the first term and r is the common ratio,
we see that,
r = 6,
the first term is,
a_1 = (x-6)
the 2nd term is,
a_2 = 3x,
the 3rd term is,
a_3 = y, finding y,
first we find x, using the above given formula we have,
\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)
x = 12,
Now, for y we can use the relation between a_3 and a_2,
\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)
y = 216
Write a general formula to describe the variation. M varies directly with the square of d and inversely with the square root of x; M=12 when d=3 and x=4
Answers
Given that 'M' varies directly with the square of 'd',
\(M\propto d^2\)Given that 'M' varies inversely with the square root of 'x',
\(M\propto\frac{1}{\sqrt[]{x}}\)Combining the relationships,
\(M\propto\frac{d^2}{\sqrt[]{x}}\)Let 'k' be the constant of proportionality. Then,
\(M=k\cdot\frac{d^2}{\sqrt[]{x}}\)Given that M=12 when d=3 and x=4,
\(\begin{gathered} 12=k\cdot\frac{(3)^2}{\sqrt[]{4}} \\ 12=k\cdot\frac{9}{2} \\ k=\frac{12\cdot2}{9} \\ k=\frac{8}{3} \end{gathered}\)Substitute the value of this constant in the general expression,
\(M=\frac{8}{3}\cdot\frac{d^2}{\sqrt[]{x}}\)Thus, the required general formula to describe the relation is obtained as,
\(M=\frac{8}{3}\cdot\frac{d^2}{\sqrt[]{x}}\)What is the opposite reciprocal of 2/3?
Answers
Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.
Step-by-step explanation:
Redondear 2,325 a la unidad de millar más cercana.
0
X
3
Answers
When 2, 325 is rounded to the nearest thousand, the result would be 2, 000.
How to round numbers to the nearest thousand ?To round a number to the nearest thousand, identify the place value of the rounding digit, which is the thousandth place (the third digit from the right).
Then, look at the digit to the right of the rounding digit. If this digit is 5 or greater, then round up the rounding digit by adding one to it. If the digit is less than 5, keep the rounding digit as it is.
The number 2, 325 would therefore be rounded to 2, 000 because the digit " 3 " is less than 5.
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A triangle on a sphere could have
degrees.
Answers
True
Explanation:
$1000 is invested at 2.9% annual interest for 6 months.
a. Simple Interest b. Compound Interest
Answers
Answer:
a. Simple interest = $174
b. Compund interest = $1187.1
Step-by-step explanation:
Given the following data;
Principal, P = $1000
Interest, R = 2.9%
Time, T = 6 months
a. To find the simple interest;
S.I = (PRT)/100
S.I = (1000*2.9*6)/100
S.I = 17400/100
S.I = $174
b. To find the compound interest;
\( A = P(1 + \frac{r}{100})^{t}\)
Substituting into the formula, we have;
\( A = 1000(1 + \frac{2.9}{100})^{6}\)
\( A = 1000(1 + 0.029)^{6} \)
\( A = 1000(1.029)^{6} \)
\( A = 1000(1.1871)\)
A = $1187.1
toss two dice. the probability of rolling an even number on both sides is 1/2x1/2= 1/4. predict in 120 tosses how many times an even number will appear on both dice?
Answers
Answer:
Chances of both even number = 30 times
Step-by-step explanation:
Given:
Chances of both even number = 1/4
Total number of tosses = 120
Find:
How many times both dice show even number
Computation:
Chances of both even number = [Chances of both even number][Total number of tosses]
Chances of both even number = 1/4 [120]
Chances of both even number = 30 times
Solve.
L. There was already 14 in. of snow on the ground when the blizzard started.
Each hour for the next 8 hours, 2.5 in. of snow fell. How much snow was
on the ground at the end of each hour?
Answers
Answer:
16.5, 19, 21.5, 24, 26.5, 29, 31.5, 34,
Step-by-step explanation:
each hour it increases by 2.5 inches and this is how much in each hour
Answer:
h1= 16.5
h2= 19
h3= 21.5
h4= 24
h5= 26.5
h6=29
h7=31.5
h8= 34
Step-by-step explanation:
start by making an equation to model the scenario then solve for each hour
f(h)=2.5h+14
In the summer reading program, a participant earns 50 stars for reading 10 books. The library tracks the number of stars (y, vertical
axis) and books (x, horizontal axis) on a graph. Which statements are correct?
A)
Point (5, 1) represents the unit rate.
B)
Point (1,5) represents the unit rate.
9
Point (0, 50) represents the unit rate.
D)
Point (100, 20) represents reading 20 books.
E)
Point (20, 100) represents reading 20 books
Answers
Answer:b and e
Step-by-step explanation:
Answer:
B and E
Step-by-step explanation:
This is because (1,5) represents the unit rate whilst, (20,100) represents reading 20 books.
MAKE SURE TO DRINK WATER AND A BREAK!!!
THINGS WILL GET BETTER <3
Pls answer quick and small explanation quick for brainlessiest answer
Answers
Answer:
Your answer is C.
exponential is to the power of a value and hence c meets the requirements
GEOMETRY 100 POINTS
Find the length of BC
Answers
Answer:
x = 16
Step-by-step explanation:
Opposite sides are equal in a parallelogram
AD = BC
5x - 12 = 3x + 20
5x - 3x = 20 + 12
2x = 32
x = 32/2
x = 16
Suppose the only measuring cup you own is a one-third measuring cup. Using this measuring cup how many scoops will you need to have 3 2/3 cups of sugar
Answers
Answer:
11
Step-by-step explanation:
for each full cup of sugar, you need 3 one-third measuring cups.
we have 3 full cups so 3×3=9
and another 2 for the 2/3, 9+2=11
so a total of 11 scoops
what is 1 1/8 add 2 4/8 =
Answers
Answer:
29/8 or 3 5/8
Step-by-step explanation:
Can someone explain this to me? Pls
Answers
Step-by-step explanation:
In Triangle (the symbolΔ)QRS,
Angle R is congruent to Angle Q,
And side QR=11
And side SQ=8
Find.The length of RS.
Help quick please look at pic to solve
Answers
The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.
Given the diagram of the hanger which one side has 10 + 5x and other side has 11.
To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.
Thus, the equation is 10 + 5x = 11.
Consider the equation 10 + 5x = 11
On subtracting 10 from each side gives,
5x = 1
Divide each side by 5 gives,
x = 1/5.
Hence, the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.
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una persona tiene 6 chaquetas y 10 pantalones. de cuántas formas distintas puede combinar estas prendas?
Answers
The total number of combinations is given as follows:
60.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways for one experiment and n ways for another experiment, then there are m x n ways in which the two experiments can happen simultaneously.
This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual experiment, according to the equation presented as follows:
\(N = n_1 \times n_2 \times \cdots \times n_n\)
The parameters for this problem are given as follows:
\(n_1 = 6, n_2 = 10\)
Hence the total number of combinations is given as follows:
6 x 10 = 60.
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five positive consecutive integers starting with a have an arithmetic mean of b. what is the arithmetic mean of 5 consecutive integers that start with b? (a) a 3 (b) a 4 (c) a 5 (d) a 6 (e) a 7
Answers
the arithmetic mean of the five consecutive integers starting with "b" is (a+4), which is option (c).
Let's call the five consecutive integers starting with "a" as a, a+1, a+2, a+3, and a+4.
The arithmetic mean of these five integers can be calculated as (a + (a+1) + (a+2) + (a+3) + (a+4))/5 = b. Simplifying this expression, we get:
5a + 10 = 5b +
a + 2 = b
So, the arithmetic mean of the five consecutive integers starting with "b" would be:
(b + (b+1) + (b+2) + (b+3) + (b+4))/5
= (5b + 10)/5 (since the integers are consecutive, we can express them in terms of b)
= b + 2
Substituting b = a + 2 (from the above equation), we get:
b + 2 = a + 4
Therefore, the arithmetic mean of the five consecutive integers starting with "b" is (a+4), which is option (c).
In other words, if the arithmetic mean of five consecutive integers starting with "a" is "b", then the arithmetic mean of five consecutive integers starting with "b" is two more than the last integer of the five consecutive integers starting with "a".
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Jacob is going on a vacation to Australia. His flight leaves at 1:15 P.M. It takes 1 hour to get to the airport, and Jacob wants to be at the airport 1 hour and 15 minutes before his flight leaves. What is the latest time that Jacob can leave for the airport?
Plzzzz help
Answers
Answer:
The latest time is 12:00
Step-by-step explanation:
take an hour away for 1:15 which is gonna be 12:15 then take the 15 minutes away and you get 12:00
Answer:
11:00
Step-by-step explanation:
if he leaves at 11:00 it’s takes an hour to get there. So when he gets there it’s 12:00 Add an hour 15 and you get 1:15
What is the area of ABCDE?____sq cm
got very confused on this part
Answers
Answer:
A= 30 sq. cm
Step-by-step explanation:
We want to find the area of both triangles seprately than add them together. For the area of a traingle, we use the equation 1/2 base times height. For triangle ABE we do this:
\(A = \frac{1}{2} (12)(4)\)
\(A = (6) (4)\)
\(A = 24\)
For triangle BDC, we do this:
\(A = \frac{1}{2} (6) (2)\)
\(A = (3) (2)\)
\(A=6\)
Now we have to add both areas ot get A=30 sq cm
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The diameter of a circle is 10 3/4 inches.
What is the radius, r, of the circle?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
Answer: The radius of the circle is 5 3/8 inches.
Step-by-step explanation:
The radius of the circle is half of the diameter. We can start by converting the mixed number diameter to an improper fraction:
10 3/4 = (10 × 4 + 3)/4 = 43/4
So, the diameter of the circle is 43/4 inches. The radius is half of this, which we can find by dividing by 2:
r = (43/4) ÷ 2 = 43/8
To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 1:
r = 43/8 = 5 3/8
Therefore, the radius of the circle is 5 3/8 inches.
Answer:5 3/4
Step-by-step explanation:
10 3/4 * 1/2
1/2 * 43/4 = 43/8
8/43=5 3/4
What is an equation of the line that passes through the point ) (8,−5) and is parallel to the line
5x+4y=24?
Answers
By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.
The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.
To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.
Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.
Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.
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An open box is made from a square piece of sheet metal 28 inches on a side by cutting identical squares fron the corners and turning up the sides. Express the volume of the box, V, as a function of the length of the side of the square cut from each corner, x.
Answers
The volume of the box, V, can be expressed as a function of the length of the side of the square cut from each corner, x, by the equation: V(x) = 4x^3 - 56x^2 + 784x.
How to find the volume?If x inches are cut from each corner of the square piece of metal, then the length of each side of the base of the box is (28 - 2x) inches, and the height of the box is x inches. The volume of the box can be expressed as the product of the area of the base and the height:
V = (28 - 2x)^2 * x
Expanding the square, we get:
V = x * (784 - 56x + 4x^2)
Simplifying, we get:
V = 4x^3 - 56x^2 + 784x
Therefore, the volume of the box, V, can be expressed as a function of the length of the side of the square cut from each corner, x, by the equation:
V(x) = 4x^3 - 56x^2 + 784x.
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sara bought 500ml milk bottle if she drink 25% of milk how much ml of milk would be left?
Answers
Answer:
500×(25÷100)=125 This is what she drank
500-125=375
she will be left with 375ml
if anyone is available please help me or comment it'll be helpful
Answers
To determine which mixture will use more salt, you have to calculate the salt-water ratio for both mixtures and compare them.
For mixture A
To calculate the ratio you have to do as follows:
\(m=\frac{8.72-5}{7-4}=\frac{5}{4}=1.25\)We can express the relationship between the amount of water and the amount of salt as:
\(y=1.25x\)y represents the number of cups of water and x represents the number of teaspoons of salt.
The calculated value 1.25 indicates that for every teaspoon of salt there is 1.25cups of water.
to determine how much salt there will be in 10 cups of water for mixture A, you have to calculate the value of x for y=10 using the equation:
\(\begin{gathered} y=1.25x \\ 10=1.25x \\ x=\frac{10}{1.25} \\ x=8 \end{gathered}\)For mixture A, there will be 8 teaspoons of salt for 10 cups of water.
Mixture B
The relationship between the cups of water and teaspoons of salt is given by the equation:
\(y=2.5x\)The coeficient that multiplies the x term indicates that for every teaspoon of salt, the mix has 2.5 cups of water. To determine the amount of salt for 10 cups of water you have to replace the formula for y=10 and calculate x:
\(\begin{gathered} y=2.5x \\ 10=2.5x \\ x=\frac{10}{2.5} \\ x=4 \end{gathered}\)This indicates that for every 10 cups of water, mixture B has 4 teaspoons of salt.
Mixture A uses more salt than mixture B.
Graphs of a function and its inverse are shown on the same coordinate grid.
Which statements accurately compare the function and its inverse? Check all that apply.
The domains of the two functions extend to positive infinity.
The ranges of the two functions are all real numbers.
The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.
The point of intersection of the two functions indicates that the functions are inverses.
Neither function has a minimum.
Answers
The correct statements are;
The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.
The point of intersection of the two functions indicates that the functions are inverses.
Option C and D
How to determine the correct statementsTo accurately compare a function and its inverse based on the graphs, we have to know the following;
The domains of the two functions extend to positive infinity if the domain of the inverse function is equivalent to the range of the original function.The ranges of the two functions are all real numbers if the graphs cover the entire y-axis without any gaps or discontinuities.If the graphs intersect at the point (a, b), it means that f(a) = b and f^(-1)(b) = a, indicating that the functions are inverses of each other.
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Find the value of x.
(x + 8)
Answers
x = 52
Explanation:
In an equilateral triangle, each angle measures 60°.
Therefore, (x + 8)° = 60°
Hence, x = 52.
I would appreciate it if you mark my answer as brainliest.
Answer:
52°
Step-by-step explanation:
This is an equilateral triangle. Therefore all the sides and angles are equal to each other.
We know that,
the sum of the interior angles in a triangle is 180° and in equilateral triangles each angle measured 60° ( 180°/3 ).
Accordingly,
x + 8 = 60
Subtract 8 from both sides.
x = 60 - 8
x = 52°
find f(g(1)) if f(x)=4x and g(x)=2x+5
Answers
Evaluating the composition of functions in x = 1 gives:
f(g(1)) = 28
How to find the composition of functions?Here we have the two functions:
f(x) = 4x
g(x) = 2x + 5
And we want to find to find the composition f(g(x)), we will get:
f(g(x)) = 4*g(x)
Replacing g(x) there we will get:
f(g(x)) = 4*(2x + 5)
= 8x + 20
Now we can evaluate that in x = 1, then we will get:
f(g(1)) = 8*1 + 20 = 28
That is what we wanted to find.
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