Right now, Miquel is 9 kilometers into a 36-kilometer race. He is running an average
of 18 kilometers every hour.
rate of change
Answer: The rate of change for Miquel's position in the race can be calculated by his speed, which is 18 kilometers per hour. So, his rate of change is 18 kilometers per hour. This means that for every hour that passes, Miquel will have covered 18 kilometers in the race.
Step-by-step explanation:
which of the following are true statements? (check all that apply)
The variable y does not vary directly with x is wrong since when x increases by 1 unit y increases by 1/2 unit for all real x.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
Given that line passes through (0,0) and (2,1)
(Note that any two points are sufficient to determine the equation of the line)
The slope = change in y/change in x
= (1-0)/(2-0)
= 1/2
Hence answers are:
Variable y varies directly with x. (if x increases y also increases and vice versa)
The constant of variation = slope of line = 1/2
The constant of variation is 2 is wrong since slope = 1/2
The variable y does not vary directly with x is wrong since when x increases by 1 unit y increases by 1/2 unit for all real x.
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evaluate a - c ÷ 6 if a = 6 and c = 12
Answer:
-1
Step-by-step explanation:
1. Plug the numbers into the equation
6-12/6
2. Solve.
6-12=-6
-6/6=-1
Answer:
4
Step-by-step explanation:
A= 6
C= 12
6-12÷6
With BIDMAS the order becomes:
6-(12÷6) —> 6-2 = 4
I need help with these questions. Excuse my failed attempts.
The measure of the angle B is found to be 184 degrees.
Explain about the co interior angles?When a transversal intersects two parallel lines, co-interior angles result between the lines. On the very same face of the transversal, the two angles always sum to 180 degrees.The angles given in question:
line AB || DC
∠B = 9x + 2
∠C = 5x - 4
So,
∠B + ∠C = 180 ( co interior angles )
9x + 2 + 5x - 4 = 180
9x - 2 = 180
9x = 180 + 2
x = 182/9
Then,
∠B = 9x + 2
∠B = 9*182/9 + 2
∠B = 182 + 2
∠B = 184
Thus, the measure of the angle B is found to be 184 degrees.
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The diagram of the correct question is attached.
What will be the
surface area of the
ramp
50 in.
60 in.
O 3672 inches squared
O 5760 inches squared
O 7392 inches squared
O 2880 inches squared
The surface area of the ramp is 3672 in².
Option A is the correct answer.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The ramp consists of three rectangular surfaces and two triangles.
Now,
Triangle.
Base = 48 in
Height = 14 in
Area of a triangle.
= 1/2 x base x height
= 1/2 x 48 x 14
= 48 x 7
= 336 in²
Rectangle.
Since the back and the bottom rectangle are not included.
Front rectangle.
Length = 50 in
Width = 60 in
Area = 50 x 60
Area = 3000 in²
Now,
The surface area of the ramp.
= 300 + 2 (336)
= 3000 + 672
= 3672 in²
Thus,
The surface area of the ramp is 3672 in².
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if Ps = 4x+8, PQ = 29, RS = 5x -3, and QR=29, then Ps=
Answer:
What is X?
Step-by-step explanation:
4 multiplied by X + 8 =Ps
I will give brainliest and ratings if you get this correct
determine whether the following function have limit or not?
The function [tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2}[/tex] has a limit
How to determine the if the function has a limit or notFrom the question, we have the following parameters that can be used in our computation:
[tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2}[/tex]
Substitute 0 for x in the above expression
So, we have the following representation
[tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2} = \frac{1 - \sqrt[3]{0^2 + 1}}{0^2}[/tex]
Evaluate the expression
[tex]\lim_{x \to 0} \frac{1 - \sqrt[3]{x^2 + 1}}{x^2}=\infty[/tex]
This means that the limit of the expression is to infinity
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Find the x- and y-intercepts of the graph of 2x - 3y = 30 State each answer as an integer or an improper fraction in simplest form.
x int = 15
y int = -10
y intercept can be found bt setting X to 0
x intercept can be found by setting Y to 0
2(0) - 3y = 30 --> -3y = 30 --> y = -10
2x - 3(0) = 30 --> 2x = 30 --> x = 15
alternatively, y int is "b" in eq. y = mx + b
-3y = 30 -2×
y = -10 + (2/3)x
y = (2/3)x - 10
b = -10
Which pair of values are equivalent? choose two correct answers
Answer:
first 2 pairs
Step-by-step explanation:
[tex]\frac{6}{100}[/tex] = 6 ÷ 100 = 0.06 ← equivalent
[tex]\frac{7}{10}[/tex] = 7 ÷ 10 = 0.7 ← equivalent
[tex]\frac{5}{10}[/tex] = 5 ÷ 10 = 0.5 ≠ 0.05
[tex]\frac{32}{100}[/tex] = 32 ÷ 100 = 0.32 ≠ 3.2
find all roots of f(x): f(x) = 6x^3-x^2-9x+4 if (2x-1) is a factor. Show all work.
Which procedure would you take first? Synthetic division?
And if its synthetic division, can you show how you divide by (2x-1)?
Answer:
[tex]x=\dfrac{1}{2},\;\;x=1,\;\;x=-\dfrac{4}{3}[/tex]
Step-by-step explanation:
Given polynomial function:
[tex]f(x) = 6x^3-x^2-9x+4[/tex]
If (2x - 1) is a factor of the given function, then 2x - 1 = 0.
Therefore:
[tex]\implies 2x-1=0[/tex]
[tex]\implies x=\dfrac{1}{2}[/tex]
To divide the given function by the factor (2x - 1), we can perform synthetic division.
As the leading coefficient of the divisor is not 1, divide the dividend and divisor by the leading coefficient of the divisor (2):
[tex]\textsf{Dividend}: \quad 3x^3-\dfrac{1}{2}x^2-\dfrac{9}{2}x+2[/tex]
[tex]\textsf{Divisor}: \quad \left(x-\dfrac{1}{2}\right)[/tex]
Perform Synthetic Division
Place ¹/₂ in the division box.
Write the coefficients of the dividend in descending order.
(Note: As no terms are missing, we do not need to use any zeros to fill in missing terms).
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\end{array}[/tex]
Bring the leading coefficient straight down:
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}&\downarrow&&&\\\cline{2-5}&3\end{array}[/tex]
Multiply the number you brought down with the number in the division box and put the result in the next column (under the -¹/₂ ):
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&\frac{3}{2}&&\\\cline{2-5}&3\end{array}[/tex]
Add the two numbers together and put the result in the bottom row:
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&&\\\cline{2-5}&3&1\end{array}[/tex]
Repeat:
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&\frac{1}{2}&\\\cline{2-5}&3&1&-4\end{array}[/tex]
[tex]\begin{array}{c|crrr}\vphantom{\dfrac12}\frac{1}{2} & 3 & -\frac{1}{2}& -\frac{9}{2} & 2\\\cline{1-1}\vphantom{\dfrac12}&\downarrow&-\frac{3}{2}&\frac{1}{2}&-2\\\cline{2-5}&3&1&-4&0\end{array}[/tex]
The bottom row (except the last number) gives the coefficients of the quotient. The degree of the quotient is one less than that of the dividend.
The last number in the bottom row is the remainder.
Therefore, the factored function after synthetic division is:
[tex]f(x)=(2x-1)(3x^2+x-4)[/tex]
The quadratic factor can be factored further:
[tex]\implies 3x^2+4x-3x-4[/tex]
[tex]\implies x(3x+4)-1(3x+4)[/tex]
[tex]\implies (x-1)(3x+4)[/tex]
Therefore, the fully factored function is:
[tex]f(x)=(2x-1)(x-1)(3x+4)[/tex]
To find the roots of the function, set each factor to zero and solve for x:
[tex]2x-1=0 \implies x=\dfrac{1}{2}[/tex]
[tex]x-1=0 \implies x=1[/tex]
[tex]3x+4=0 \implies x=-\dfrac{4}{3}[/tex]
Therefore, the roots of the given function are:
[tex]x=\dfrac{1}{2},\;\;x=1,\;\;x=-\dfrac{4}{3}[/tex]
I need help it’s 9th grade algebra 1
The system of equations has one solution, which is (2, 3).
What is the Solution to the Graphed System of Equations?To find the solution to a graphed system of equations, you need to find the points where the graphs of the two equations intersect. These points represent the coordinates of the solution, which are the values of x and y that make both equations true simultaneously.
The system of equations as shown in the graph has one solution, which is: (2, 3). This is because the liens intersect at the point (2, 3).
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In order to reduce your end-of-season inventory of gloves, you create grab bags that each contain 2 pairs of gloves. You have 20 pairs of lined gloves that cost $25 and 100 pairs of knit gloves that cost $12. Your assistant made 60 grab bags wheres 2 bags have two pairs of lined gloves 16 bags have one pair of lined gloves and one pair of knit gloves and 42 bags have two pairs of knit gloves.
Compute the expected value of each grab bag the assistant made, rounded to the nearest 50.01_________
If you sell these for $29.99 and sell all 60 grab bags, how much total profit will you make? Give your answer to the nearest 50.01
The expected value of each grab bag is $1.67 for two pairs of lined gloves, $9.87 for one pair of lined gloves and one pair of knit gloves, and $16.80 for two pairs of knit gloves. the total profit made from selling all 60 grab bags is $149.40.
For the 2 bags that have two pairs of lined gloves, the total cost is:
2 pairs * $25/pair = $50
Total gloves = 4
For the 16 bags that have one pair of lined gloves and one pair of knit gloves, the total cost is:
1 pair lined gloves * $25/pair + 1 pair knit gloves * $12/pair = $37
Total gloves = 4
For the 42 bags that have two pairs of knit gloves, the total cost is:
2 pairs * $12/pair = $24
Total gloves = 4
The probability of selecting a bag with two pairs of lined gloves is:
2/60 = 1/30
The probability of selecting a bag with one pair of lined gloves and one pair of knit gloves is:
16/60 = 4/15
The probability of selecting a bag with two pairs of knit gloves is:
42/60 = 7/10
The expected value of a bag with two pairs of lined gloves is:
(1/30) * $50 + (0) * $37 + (0) * $24 = $1.67
The expected value of a bag with one pair of lined gloves and one pair of knit gloves is:
(4/15) * $37 + (0) * $50 + (0) * $24 = $9.87
The expected value of a bag with two pairs of knit gloves is:
(7/10) * $24 + (0) * $50 + (0) * $37 = $16.80
The total cost of the gloves used to make the grab bags is:
2 bags * $50/bag + 16 bags * $37/bag + 42 bags * $24/bag = $1,650
The total revenue from selling all 60 grab bags is:
60 bags * $29.99/bag = $1,799.40
Therefore, the total profit is:
$1,799.40 - $1,650 = $149.40
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monica works at bakery and is making a large rectangelar cake the customer requested that half of the cake be frosted with vanila icing and the other half be frosted with chocalate icing the customer also want ssprinkles on 2/3 of the vanilla half and on 1/4 choclate
Answer: Let's call the length of the cake "l" and the width of the cake "w". The total area of the cake would be l * w.
Half of the cake is frosted with vanilla icing, so the area of the vanilla half would be (l * w) / 2.
And 2/3 of the vanilla half is to be covered with sprinkles, so the area covered with sprinkles would be (l * w) / 2 * 2/3 = (l * w) / 3.
The other half of the cake is frosted with chocolate icing, so the area of the chocolate half would be (l * w) / 2.
And 1/4 of the chocolate half is to be covered with sprinkles, so the area covered with sprinkles would be (l * w) / 2 * 1/4 = (l * w) / 4.
So, the total area of the cake covered with sprinkles would be (l * w) / 3 + (l * w) / 4.
Step-by-step explanation:
Factorise the following:
a) x² + 4x + 4
b) x²- 12x + 27
c) x²-x-42
d) x² + 8x-9
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A
[tex]x^2+4x+4\\\rightarrow x^2+2x+2x+4\\\rightarrow x(x+2)+2(x+2)\\\rightarrow (x+2)(x+2)[/tex]
Part B
[tex]x^2-12x+27\\\rightarrow x^2-9x-3x+27\\\rightarrow x(x-9)-3(x-9)\\\rightarrow (x-3)(x-9)[/tex]
Part C
[tex]x^2-x-42\\\rightarrow x^2+6x-7x-42\\\rightarrow x(x+6)-7(x+6)\\\rightarrow (x-7)(x+6)[/tex]
Part D
[tex]x^2+8x-9\\\rightarrow x^2+9x-x-9\\\rightarrow x(x+9)-1(x+9)\\\rightarrow (x-1)(x+9)[/tex]
Cricket is a sport played with a ball and a rectangular bat. Players protect themselves with batting gloves and other equipment. The table shows the weights, in pounds, of several pieces of cricket equipment. CRICKET EQUIPMENT Equipment Ball Glove Bat Weight (pounds) 0.35 0.77 2.63 A cricket bag holds 4 balls, 2 gloves, and 2 bats. What is the total weight, in pounds, of the balls, gloves, and bats in the cricket bag? Show your work.
The total weight in the bag is given as follows:
8.2 pounds.
How to obtain the total weight?The total weight is obtained applying the proportions in the context of the problem.
From the table, the weight of each equipment is given as follows:
Ball: 0.35 pounds.Glove: 0.77 pounds.Bat: 2.63 pounds.Hence the total weight of a bag with 4 balls, 2 gloves, and 2 bats is given as follows:
4 x 0.35 + 2 x 0.77 + 2 x 2.63 = 8.2 pounds.
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-8c + 13 ≥ 47 solve the inequality
Answer: c[tex]\leq[/tex]-17/4
Step-by-step explanation:
-8c+13[tex]\geq[/tex]47
-8c[tex]\geq[/tex]47-13
-8c[tex]\geq[/tex]34
c[tex]\leq[/tex] -17/4 or -4 1/4
61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94 WHAT IS THE RANGE
The value of the range is 33
How to determine the rangeFrom the question, we have the following parameters that can be used in our computation:
61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94
To find the range of a set of numbers, we need to subtract the smallest number from the largest number.
In this set of numbers:
The smallest number is 61 and the largest number is 94.
Therefore, the range of this set of numbers is:
94 - 61 = 33
Hence, the range of the given set of numbers is 33.
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Referring to the figure, evaluate the expression shown
when a = 3, b = 7, c = 2
Answer:-17
Step-by-step explanation:
b=7,then
b^2=49
square root of 49-4*3*2=-17
Find the measure of the three missing angles in the rhombus below.
Answer:
y=67
z=113
x=67
Step-by-step explanation:
opposite angles are parallel in a rhombus and they all equal 360
I don't know what answer please help quickly
The inequality changes if both sides of the expressions are switched or multiplied by a negative sign
Changing the signs of an inequality.Inequalities are expressions not separated by an equal sign.
From the given inequalities
For -10.5 < 3e
3e > -10.5
e > -10.5/3
This shows that the sign changes
For b/6≤ 7
b ≤ 6(7)
b≤ 42
The inequality sign does not change.
For the inequality -4.5c > 9
4.5c < -9
c < -9/4.5
c < -2
The inequality sign changes.
For the inequality -21/5 ≤ -5/2 d
21/5 ≥ 5/2d
5/2d≤ 21/5
d ≤42/25
The inequality sign does not change
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The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
Answer:
[tex]x=-3,x=-3,x=7[/tex]
Step-by-step explanation:
[tex]We\ know\ that\ the\ roots\ of\ an\ equation\ are\ its\ intercepts\ cut\ on\ the\ x-axis.\\We\ can\ observe\ that\ the\ graph\ of\ y=f(x)\ cuts\ the\ x\ axis\ at\ the\ point (7,0)\\ and\ touches\ the\ x-axis\ at\ (-3,0).\\[/tex]
[tex]Hence,\\The\ curve\ represents\ a\ cubic\ polynomial\ with\ double\ roots\ (-3,0),(-3,0)\\ as\ well\ as\ a\ distinct\ root:\ (7,0)[/tex]
Divide 10a6b4 by 5a2b.
2a8b5
2a4b5
2a4b4
2a4b3
Answer: 2a^4b^3
Step-by-step explanation: Divide the base like normal. Subtract the exponents.
a6 - a2 = a4
b4 - b = b3
A single variable will always equal to 1 so b will be its own exponent.
After divide the solution is,
⇒ 2a⁴b³
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
Divide 10a⁶b⁴ by 5a²b.
Hence, We get;
⇒ 10a⁶b⁴ / 5a²b.
⇒ 2a⁶⁻² b⁴⁻¹
⇒ 2a⁴b³
Thus, After divide the solution is,
⇒ 2a⁴b³
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Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = 0.7 and P(B) = 0.4.
A. Could it be the case that P(A ∩ B) = 0.5? Pick one:
i. Yes, this is possible. Since B is contained in the event A ∩ B, it must be the case that P(B) ≤ P(A ∩ B) and 0.5 > 0.4 does not violate this requirement.
ii. Yes, this is possible. Since A ∩ B is contained in the event B, it must be the case that P(B) ≤ P(A ∩ B) and 0.5 > 0.4 does not violate this requirement.
iii. No, this is not possible. Since B is equal to A ∩ B, it must be the case that P(A ∩ B) = P(B). However 0.5 > 0.4 violates this requirement.
iiii. No, this is not possible. Since B is contained in the event A ∩ B, it must be the case that P(A ∩ B) ≤ P(B). However 0.5 > 0.4 violates this requirement.
v. No, this is not possible. Since A ∩ B is contained in the event B, it must be the case that P(A ∩ B) ≤ P(B). However 0.5 > 0.4 violates this requirement.
B. From now on, suppose that P(A ∩ B) = 0.3. What is the probability that the selected student has at least one of these two types of cards?
C. What is the probability that the selected student has neither type of card?
D. In terms of A and B, the event that the selected student has a Visa card but not a MasterCard is A ∩ B' . Calculate the probability of this event.
E. Calculate the probability that the selected student has exactly one of the two types of cards.
Option A. No, this is not possible. Since A and B are not mutually exclusive events, we have P(A ∩ B) = P(A) + P(B) - P(A ∪ B), where P(A ∪ B) is the probability that the selected student has either a Visa or a MasterCard.
Since 0.5 > 1 - P(A ∪ B) = P(A') ∩ P(B'), we must have P(A') ∩ P(B') < 0, which is impossible.
B. The probability that the selected student has at least one of these two types of cards is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.7 + 0.4 - 0.3 = 0.8.
C. The probability that the selected student has neither type of card is given by P(A' ∩ B') = 1 - P(A ∪ B) = 1 - 0.8 = 0.2.
D. The probability of the event A ∩ B' is given by P(A ∩ B') = P(A) - P(A ∩ B) = 0.7 - 0.3 = 0.4.
E. The probability that the selected student has exactly one of the two types of cards is given by P((A ∩ B') ∪ (A' ∩ B)) = P(A ∩ B') + P(A' ∩ B) = 0.4 + 0.1 = 0.5.
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8. At a home supply store, bags of concrete mix are on sale. Every third bag that you buy is discounted by 75%. A bag of concrete mix sells for $3.88. How much will you spend if you buy 14 bags of concrete mix? 75
The total amount spend is 391.88
What is discount?The noun discount refers to an amount or percentage deducted from the normal selling price of something.
If 14 bag of mix cement are bought and and every third bag is discounted
no of bag on discount = 14/3 = 4 remainder 2
therefore 4 bags will be on discount
discount on a bag = 3.88× 75/100
= 291/100 = 2.91
therefore each bag on discount will cost = 3.88 - 2.91
= 0.97
for 4 bags = 0.97 ×4 = 3.88
for remaining 10 bags = 3.88 × 10
= 388
therefore the total amount = 388+3.88
= $391.88
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find the mode of the following data 20,26,16,22,20,30,22,20,26
The mode of the data 20,26,16,22,20,30,22,20,26
How to find the mode of the data?From the question, we have the following parameters that can be used in our computation:
20,26,16,22,20,30,22,20,26
The mode of a dataset is the data element that has the highest frequency
Using the above as a guide, we have the following:
20 has the highest frequency of 3
Hence, the mode is 3
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There are 9 girls and 6 boys taking golf lessons. Write the ratio that compares the number of girls taking golf lessons to the total number of students taking golf lessons.
Answer:
2:5
Step-by-step explanation:
We know
There are 9 girls and 6 boys taking golf lessons.
So, there are a total of 15 taking a golf lesson.
Write the ratio that compares the number of girls taking golf lessons to the total number of students taking golf lessons.
The ratio is
6:15 = 2:5
So, the ratio is 2:5
Using Addition to Compare Numbers
Sara and Danica are having a competition to see who
can find more recyclable cans in a month.
At the end of the first week, Sara collected 14 cans and
Danica collected 17 more cans than Sara.
The equation below represents the number of cans
Danica collected..
14+ 17 = n
Choose the answers that make the comparison
statements true.
The sum is
The sum is
The sum will be
The sum will be
more than 14.
more than 17.
14.
17.
The answer that makes the comparison statements true, The sum is more than 17. So Option B is correct.
What is addition ?Addition is a basic mathematical operation that combines two or more numbers to give a total or sum. It is one of the four elementary arithmetic operations, along with subtraction, multiplication, and division.
The equation 14+17=n represents the total number of cans Danica collected at the end of the first week, where n is the number of cans Danica collected.
We can solve for n by adding 14 and 17, which gives us:
n = 14 + 17 = 31
Therefore, Danica collected 31 cans at the end of the first week.
To make the comparison statements true:
The sum is more than 17:
This statement is true, since the sum of 14 and 17 is 31, which is greater than 17.
The sum will be 14:
This statement is false, since the sum of 14 and 17 is 31, not 14.
The sum will be 17:
This statement is false, since the sum of 14 and 17 is 31, not 17.
So, the correct answer is: The sum is greater than 17.
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For complete question image is attached:
Find the interest rate (with annual compounding) that makes the statement true. Round to the nearest tenth when necessary. $4081 grows to $8404.54 in 21 years 3.5% o 3% o 6.5% 6%
The interest rate that can explain how $4081 grew to $8404.54 in 21 years with annual compounding is option (a) 3.5%, rounded to the nearest tenth.
The interest rate and the compounding frequency determine the growth of the initial amount over time. In this problem, we need to find the interest rate that can explain how an initial amount grew to a specific amount over a certain number of years.
The problem asks us to find the interest rate that can explain how an initial amount of $4081 grew to $8404.54 in 21 years with annual compounding. We can use the formula for compound interest to solve this problem:
[tex]A = P(1 + r/n)^{nt}[/tex]
where A is the future value of the investment, P is the initial amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we know that P = $4081, A = $8404.54, n = 1 (annual compounding), and t = 21. We need to find the value of r that makes the equation true.
We can rearrange the formula to solve for r:
[tex]r = n[(A/P)^{1/nt} - 1][/tex]
Substituting the known values, we get:
[tex]r = 1[(8404.54/4081)^{1/(1*21)} - 1][/tex]
r = 0.0353 or 3.53%
This means that if the initial amount was invested with an annual interest rate of 3.5%, it would have grown to the given future value after 21 years.
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Complete the sentence that describes the slope from the graph below.
Average Minutes to Clean up a Car Accident
200
190
180 y=0.7794x-1435.5
170
160
150
140
130
120
110
100
90
80
70
60
50
Every
1970
1975
1980
1985
1990
1995
minutes.
2000 2005
after 1970, the average number of
to clean up an accident has
2010
2015
by
2020
The Average Minute to Clean up a Car is 0.7794.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The equation of the graph is y=0.7794x-1435.5.
When we compare the equation with the standard form of equation y=mx+b.
The m will be 0.7794 which means slope is 0.7794.
Hence, 0.7794 is the Average Minute to Clean up a Car.
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1. Look at the rectangle at right. Find the ratio of the shaded area to the area of the whole figure. Find the ratio of the shaded area to the unshaded area. 2. Use the figure below to find these ratios: AC/CD. CD/BD, and BD/BC
1. The ratio of the shaded area to the area of the whole figure is 3/8 and the ratio of the shaded area to the unshaded area is 3/5.
2. The value of AC/CD. CD/BD, and BD/BC is 8/5, 5/2 and 10/7 respectively.
A ratio is a comparison of two quantities, and it can be expressed in different ways, such as a fraction, a decimal, or a percentage. In this case, we will explore how to find ratios of areas in geometric figures.
Firstly, let's consider the rectangle on the right. To find the ratio of the shaded area to the area of the whole figure, we need to calculate both of these values. The shaded area is a rectangle with dimensions 6 by 2, which means its area is 6 x 2 = 12 square units.
The whole figure is a rectangle with dimensions 8 by 4, so its area is
=> 8 x 4 = 32 square units.
Therefore, the ratio of the shaded area to the area of the whole figure is 12/32, which simplifies to 3/8.
To find the ratio of the shaded area to the unshaded area, we need to subtract the shaded area from the whole area. The unshaded area is a rectangle with dimensions 8 by 2, so its area is
=> 8 x 2 = 16 square units.
Subtracting the shaded area from the whole area gives us
=> 32 - 12 = 20 square units for the unshaded area.
Thus, the ratio of the shaded area to the unshaded area is 12/20, which simplifies to 3/5.
Moving on to the second question, we need to use the figure below to find three ratios: AC/CD, CD/BD, and BD/BC.
Let's start with the first ratio, AC/CD. We know that AC is 8 units long and CD is 5 units long, so
=> AC/CD is 8/5.
Next, CD/BD. We know that BD is 10 units long, so to find CD/BD, we need to subtract the length of AC from the length of BD. AC is 8 units long, so
BD - AC = 10 - 8 = 2 units.
Therefore, CD/BD is 5/2.
Finally, BD/BC. We know that BC is 12 units long, so to find BD/BC, we need to subtract the length of CD from the length of BC. CD is 5 units long, so
=> BC - CD = 12 - 5 = 7 units.
Therefore, BD/BC is 10/7.
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