Answer: 6 [tex]\frac{17}{18}[/tex] gallons of gas left in the car
Step-by-step explanation:
Upon further clarification, this question reads "3/8 of the gas" and not "38 of the gas."
If Tom's car has 11 1/9 gallons of gas, and we want to know how much gas the car will have left if he uses 3/8 of that, we first need to find 3/8 of 11 1/9.
"Of" can usually be written as multiplication.
3/8 of 11 1/9 = 3/8 * 11 1/9 = 4 1/6
Next, we will use subtraction since he uses 4 1/6 gallons of gas.
11 1/9 - 4 1/6 = 6 17/18 gallons
PLEASE HELP!!!
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at negative 3 comma 16, a point at negative 7 comma 0, a point at 1 comma 0, a point at negative 6 comma 7, and a point at 0 comma 7.
What is the standard form of the equation of f(x)?
f(x) = −x2 − 6x + 7
f(x) = −x2 + 6x + 7
f(x) = x2 − 6x + 7
f(x) = x2 + 6x + 7
The standard form of the equation of f(x) is option a -x² - 6x + 7
Given,
The graph shows a downward open parabola.
The vertex points are:
(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)
Now,
We have to find the standard form of the function f(x):
As from the graph:
Parabola opens downward, so the function will be negative.
We have the options with:
a = -1, b = -6 and c = 7
Now,
Use x = -b/2a
x = 6/2 × -1 = 6/-2 = -3
Now,
f(x) = -x² - 6x + 7
f(-3) = -(-3)² - 6(-3) + 7
f(-3) = -9 + 18 + 7
f(-3) = 9 + 7
f(-3) = 16
That is, the points for the vertex in this equation is (-3, 16)
Then, the standard form of the equation of f(x) is option a -x² - 6x + 7
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name the rule and list the next three terms in the pattern 2,4,8,16,32...
This is Geometric progression G P
[tex]\begin{gathered} \\ 2^1=2 \\ 2^2=4 \\ 2^3=8 \\ 2^4=16 \\ 2^5=32 \\ 2^6=64 \\ 2^7=128 \\ 2^8=256 \end{gathered}[/tex]The next three terms are;
64,128,256
separate 84 into two parts such that one part will be 12 less than twice the other
Answer:
32, 52
Step-by-step explanation:
84=x+y
x=2y-12
Solving the system of equations
Plug second equation into first
84=(2y-12)+y
84=3y-12
y=32
Plug y into first equation
84=x+32
x=52
For which value of x does the graph of the following function F(x) have a
vertical asymptote?
F(x) =
1
X-11
Answer:
x = 1
Step-by-step explanation:
Horizontal asymptotes are the y-values for which a particular function is undefined;
Finding the horizontal asymptote for linear reciprocal function is quite simple;
For this kind of function, where there is no x term in the numerator, the horizontal asymptote is just equivalent to the constant added to the fraction (note: having no added constant is the same as having an added 0);
so:
f(x) = 1/(x - 1) = (1/( - 1 )) + 0
The horizontal asymptote is y = 0 for this function.
If it was F(x) = (1/(x - 1)) + 1, the horizontal asymptote would be y = 1
hope it help!! :)
what is the answer to 8x= - 44 ?
We need to solve the following equation for x:
[tex]8x=-44[/tex]To isolate x, we divide both sides
The cost (in dollars) of a basic music streaming service for m months
is represented by B(m) = 5m. The cost of the premium service is represented by
P(m) 10m. Describe the transformation from the graph of B to the graph of P.
The transformation from the graph of B to the graph of P is a vertical stretch by a scale factor of 2
How to determine the transformation?From the question, the function definitions are given as
B(m) = 5m
P(m) = 10m
Rewrite the function P(m) as follows
P(m) = 2 x 5m
Substitute B(m) = 5m in the equation P(m) = 2 x 5m
P(m) = 2 x B(m)
When a function is represented as
f(x) = kg(x), then the transformation is a vertical stretch by k
Hence. the transformation a vertical stretch by 2
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please answer fast!!!!! find x
Step-by-step explanation:
the triangles are congruent out at least similar, so both have the same angles.
therefore,
2x = 80
x = 40
4(8g+5)+6
I thought the answer was 32g+26 but its not on there
Answer:
32g + 6(you got it right, not quite sure why it isn't there though!)
Step-by-step explanation:
remember PEMDAS
parentheses first
(8g+5) but we can't add them up since they not like terms
now we go from left to right (since we have Multiplication first and then Addition)
distribute the 4 to the (8g+5)
which makes it 32g +20
now we go back to the equation,
32g +20 + 6
are there any like terms we can combine?
yes, the 20 and the 6
20+6=26
leaving us with
32g + 265. Which expression does not have a value of 3?
å
O
O
-16-(-11)
19-16
-13-(-16)
1-(-2)
By driving 10 miles per hour faster, Goldie was able to
Ishave 2 hours and 30 minutes off her 50-mile trip to visit
her grandmother who lives in the mountains. Select the
equation that could be used to solve this problem. Use x to
represent her faster driving rate.
The faster driving rate of Goldie is 20 miles/hour.
Given that, by driving 10 miles per hour faster, Goldie was able to have 2 hours and 30 minutes off her 50-mile trip.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Here, Speed = 10 miles/hour, Time = 2 hours and 30 minutes = 2.5 hours and Distance = 50 mile.
Now, Distance = Speed × Time
Let the faster driving rate be x.
50 = x × 2.5
⇒ x = 50/2.5
⇒ x = 20 miles/hour
Therefore, the faster driving rate of Goldie is 20 miles/hour.
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Answer:
Step-by-step explanation:
I don't agree with the other answer.
You need to you systems of equations
So
d=50 t=t-2.5 x=r+10
d=rt
50=(r+10)(t-2.5) (faster equation)
50=rt (slower equation)
t=[tex]\frac{50}{r}[/tex] (substitute into faster equation)
50 = (r+10)(50/r -2.5) mult both sides by r to get rid of fraction
50r = (r+10)(50-2.5r) FOIL
50r = 50r -2.5r² + 500 -25r Simplify
2.5r²+25r-500=0 divide all by 2.5
r²+10r-200 factor
(r-20)(r+10) eliminate negative answer
r=20
x=r+10 =20+10 =30 mph
You and a friend have each randomly draw a card.
There are 52 cards in a deck.
There are 12 face cards in the deck, that is 3 face cards per suit.
The probability of getting at least from two draws is given to be:
[tex]P=P(X=1)+P(X=2)[/tex]Therefore, the probability is calculated using the formula:
[tex]P=\frac{^{12}C_1\times^{40}C_1}{^{52}C_2}+\frac{^{12}C_2}{^{52}C_2}[/tex]Using the combination formula, we have the solution to be:
[tex]\begin{gathered} \Rightarrow\frac{12\times40}{1326}+\frac{66}{1326}=\frac{480}{1326}+\frac{66}{1326} \\ P=\frac{546}{1326} \\ P=\frac{7}{17} \end{gathered}[/tex]The LAST OPTION is correct.
A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation of the hyperbola?show steps
The standard form of a hyperbola with center (h,k) is
We know the vertices are at (5,0) and (-5,0)
The vertices are at (h+a,k) and ( h-a,k)
The center must be at (0,0) and the a value is 5
The coordinates of the foci are at ( h+c,k) and ( h-c, k) and we know one of the foci is at (6,0)
c is equal to 6
We know that c^2 = a^2+b^2
6^2 = 5^2 + b^2
36 = 25+b^2
11 = b^2
We can write the equation
can you show how to solve this proplem
In the given figure : lines l and m are parallel and a, b are transversal
Since, the lines a and b are parallel and l act as a transversal.
Then,
[tex]\begin{gathered} \angle BAC=\angle ACb\text{ (alternate interior angles)} \\ \text{ Substitute the values} \\ 2x=46 \\ x=\frac{46}{2} \\ x=23 \end{gathered}[/tex]x = 23
Answer : x = 23
PLS HELP ASAP (100 POINTS) The line of best fit for the following data is represented by y = 0.81x + 6.9.
x y
3 9
6 9
5 13
7 13
8 16
8 11
What is the sum of the residuals? What does this tell us about the line of best fit?
A. 0.37; This indicates that the line of best fit is not very accurate and is a good model for prediction.
B. −0.37; This indicates that the line of best fit is accurate and is an overall a good model for prediction.
C. 0; This indicates that the line of best fit is very accurate and a good model for prediction.
D. 0; This indicates that the line of best fit is not very accurate and is not a good model for prediction.
Answer:
B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.Step-by-step explanation:
y = 0.81x + 6.9
residual value = Measured value - Predicted value
Measured value = actual y-coordinate of the point, y
Predicted value = value of y from the equation, y1
residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)
residual value = y - y1
x y y1 residual (y-y1)
3 9 9.33 -0.33
6 9 11.76 -2.76
5 13 10.95 2.05
7 13 12.57 0.43
8 16 13.38 2.62
8 11 13.38 - 2.38
Sum of residuals:
sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)
sum of residuals = -0.37ANSWER:
B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.
(Though not very accurate as it should have been if the sum of residuals was equal to 0).
A total discrepancy of -0.37 is not too bad.
Answer:Answer:
B. −0.37;
This indicates that the line of best fit is accurate and is an overall good model for prediction.
Step-by-step explanation:
y = 0.81x + 6.9
residual value = Measured value - Predicted value
Measured value = actual y-coordinate of the point, y
Predicted value = value of y from the equation, y1
residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)
residual value = y - y1
x y y1 residual (y-y1)
3 9 9.33 -0.33
6 9 11.76 -2.76
5 13 10.95 2.05
7 13 12.57 0.43
8 16 13.38 2.62
8 11 13.38 - 2.38
Sum of residuals:
sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)
sum of residuals = -0.37
ANSWER:
B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.
(Though not very accurate as it should have been if the sum of residuals was equal to 0).
A total discrepancy of -0.37 is not too bad.
Hannah is solving 42×19. Hannah says, “That’s easy! I can just break up the numbers and do 40×10=400 and 2×9=18.” Is Hannah correct? In the space below, show or explain why he’s correct or incorrect.
No, Hannah is incorrect.
We are given the expression 42*19.
Hannah got the solution by multiplying 40*10 and 2*9 and then adding the values.
This can be done by using distributive property, which is given by:-
(a + b)(c + d) = ac + ad + bc + bd
We can write,
42*19 = (40 + 2)(10 + 9) = 40*10 + 40*9 + 2*10 + 2*9
Hence, the answer is not just 40*10 + 2*9 but 40*10 + 40*9 + 2*10 + 2*9.
Hannah did not add the remaining 40*9 + 2*10 to calculate the answer.
That is why Hannah was incorrect.
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5-52: the first card selected from a standard 52-card deck is a king. a. if it is returned to the deck, what is the probability that a king will be drawn on the second selection? b. if the king is not replaced, what is the probability that a king will be drawn on the second selection? c. in part (b), are we assuming the card selections are independent? justify your answer.
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability.
The probability of getting a king card is 1/13 or 0.077.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: Total number of probability - 52
Now, the first selected card is king and it is returned to the deck.
So it contains no effect on the second selection card.
Then, we have to estimate probability to obtain a king
probability = favourable outcomes for a king / total possible outcomess
= 4 king cards / 52 cards in total
= 4 / 52 = 1 / 13
The probability of getting a king card is 1 / 13 or 0.077
Therefore, the correct answer is option B. 1/13, or 0.077.
The complete question is:
The first card selected from a standard 52-card deck was a king. It isreturned to the deck, what is the probability that a king will be drawn on the second selection?
A. 1/4 or 0.25
B. 1/13, or 0.077
C. 12/13, or 0.923
D. 1/3 or 0.33
E. None of the above
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Katerina runs 15 miles in 21/2 hours. What is the average number of minutes it takes her to run 1 mile?
A. 6
B. 10
C. 12 1/2
D. 16 2/3
E. 17 1/2
If Katerina completes a 15-mile run in 2 1/2 hours. She will complete a mile in an average of five minutes. Option B is correct.
What is average?It is described as a single number that indicates either the closed value for each entry in the set of data or the mean value for the entire set of data.
It is given that, In 2 1/2 hours, Katerina completes a 15-mile run.
We have to find the average number of minutes it takes her to run 1 mile.
15 miles = 2 1/2 hours
15 miles=5/2 hours
The unitary approach allows us to calculate the value of a single unit and then use that value to calculate the value of the required number of units.
1 miles= 5 /30 hours
1 miles = 1/6 hours
As we know that 1 hour consists of 60 minutes.
1 hours = 60 minute
1 mile = 60 / 6 minutes
1 miles = 10 minute
Thus, the average number of minutes it takes her to run 1 mile will be 10 minutes. Option B is correct.
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A model of a ship is made to a scale of 3:400
The surface area of the model is 7200 cm²
Calculate, in m², the surface area of the ship.
Answer:
Given:
Model : Ship = 3 : 400
The surface area of the model = 7200 cm²
To Find:
The surface area of the actual ship in m²
Let's start with the map scale given:
Model : Ship = 3 : 400
We start by adding in a unit. Usually, we choose the units associated with the model:
Model : Ship = 3 cm : 400 cm
Now, according to tot the question, we know that the actual ship is in m:
Model : Ship = 3 cm : 400 ÷ 100 m
Model : Ship = 3 cm : 4 m
The question asked for surface area, so the units have to be in squares:
Model : Ship = (3 cm)² : (4 m)
Model : Ship = 9 cm² : 16 m²
Now, that we have the units set correctly according to the question requirement, we will find 1 branch of the model:
Model : Ship = 9 cm² : 16 m²
Model : Ship = 9÷9 cm² : 16÷9 m²
Model : Ship = 1 cm² : 16/9 m²
Finally, we can find the required units by multiplying both sides with the required units:
Model : Ship = 1 cm² : 16/9 m²
Model : Ship = 1 x 7200 cm² : 16/9 x 7200 m²
Model : Ship = 7200 cm² : 12800 m²
Answer: The surface area of the ship is 12800 m²
(by the way, this was copied from the same website)
hope this helps :)
Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. The sample of 2100 bacteria selected from this population reach the size of 2249 bacteria in two and a half hours. Find the hourly growth rate parameter.This is a continuous exponential growth model.Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
In this problem, we have a continuous exponential growth model
so
the equation is of the form
[tex]y=a(e)^{kt}[/tex]where
a is the initial value ------> a=2,100
y is the number of bacteria
x ----> number of hours
so
[tex]y=2,100(e)^{kt}[/tex]For x=2.5 hours, y=2,249 bacteria
substitute
[tex]2,249=2,100(e)^{(2.5k)}[/tex]solve for k
apply ln both sides
[tex]\ln (\frac{2,249}{2,100})=2.5k\cdot\ln (e)[/tex]k=0.0274
convert to percentage
k=2.74%Hemework -13 .
Express the ratio 20cm to 15m in the form 1:n
Answer:
1: 75
Step-by-step explanation:
20cm : 15m
Convert meters to cm
1 meter = 100 cm
15m = 15 x 100 = 1500 cm
20cm:1500cm
Divide both sides of the ratio by 20
=> 1 : 1500/20 = 1: 75
The ratio of 20cm to 15m in the form 1:n is 1:75.
What is a ratio?A ratio is a mathematical comparison of two or more quantities expressed in terms of the number of times one quantity contains another quantity.
It is used to express the relationship between two or more numbers or variables and is usually written as a fraction or with a colon between the two numbers.
We have,
First, we need to convert both measurements to the same unit.
Let's convert 20cm to meters:
20 cm = 20/100 m = 0.2 m
Now we can express the ratio of 20cm to 15m as:
0.2m : 15m
To simplify this ratio, we can divide both sides by the greatest common factor of the two numbers, which is 0.1m:
0.2m/0.1m : 15m/0.1m
2 : 150
Finally, we can simplify the ratio by dividing both sides by 2:
1 : 75
Therefore,
The ratio of 20cm to 15m in the form 1:n is 1:75.
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A solution needs to contain between 46% glucose and 50% glucose. Find the least and greatest amount of a 60% glucose solution that should be mixed with a 40% glucose solution in order to
end up with 30 kilograms of a solution containing the allowable percentage of glucose.
Answer:
least: 9 kggreatest: 15 kgStep-by-step explanation:
You want the range of amounts of 60% solution that can be added to a 40% solution to achieve 30 kg of a solution that lies in the range of 46% to 50%.
SetupLet x represent the mass in kg of 60% solution added. The fraction of the total solution that is glucose will be ...
0.46 ≤ (0.60x +0.40(30 -x))/30 ≤ 0.50
SolutionMultiplying by 30 and simplifying the inequality, we have ...
13.8 ≤ 0.20x +12 ≤ 15
1.8 ≤ 0.2x ≤ 3 . . . . . . . . subtract 12
9 ≤ x ≤ 15 . . . . . . . . . . divide by 0.2
The least amount of 60% solution that should be added is 9 kg. The greatest amount is 15 kg.
__
Check
9 kg of 60% +21 kg of 40% has 5.4 +8.4 = 13.8 kg of glucose, the minimum.
15 kg of 60% +15 kg of 40% has 9 +6 = 15 kg of glucose, the maximum.
(The minimum and maximum values are seen in the solutions steps after the initial multiplication by 30.)
Question 10 of 183Consider the line y = -x +6.(a) Find the equation of the line that is parallel to this line and passes through the point (2, 6).(b) Find the equation of the line that is perpendicular to this line and passes through the point (2, 6).Note that a graphing calculator may be helpful in checking your answer.
Answer:
Part A:
[tex]y=-x+8[/tex]Part B:
[tex]y=x+4[/tex]Step-by-step explanation:
Part A:
Remember that two parallel lines have the same slope. This way, we can conclude that the slope of this particular line is:
[tex]m_a=-1[/tex]Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:
[tex]\begin{gathered} y-6=-1(x-2) \\ \rightarrow y-6=-x+2 \\ \\ \Rightarrow y=-x+8 \end{gathered}[/tex]Therefore, we can conclude that the equation of this line is:
[tex]y=-x+8[/tex]Part B:
Remember that the product between the slopes of two perpendicular lines is -1. This way, we'll have that:
[tex]\begin{gathered} -1\times m_2=-1 \\ \\ \Rightarrow m_2=1 \end{gathered}[/tex]Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:
[tex]\begin{gathered} y-6=(x-2) \\ \rightarrow y=x+4 \end{gathered}[/tex]Therefore, we can conclude that the equation of this line is:
[tex]y=x+4[/tex]The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011$5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year (d) Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of P0 and d to the nearest dollar.Pt= (e) Using the regression model, predict the cost of insurance in 2030.$ (f) According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year
Part (a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).
we have the ordered pairs
(1999, 2,196) -------> (0,2,196)
(2019,7,186) -------> (20,7,196)
Find out the slope
where
t -----> is the number of years since 1999
P ----> the cost
m=(7,196-2,196)/(20-0)
m=5,000/20
m=250
Find the equation of the linear model in slope-intercept form
P=mt+b
we have
m=250
point (0,2,196)
substitute and solve for b
2,196=250(0)+b
b=2,196
therefore
P=250t+2,196
Part b
Using this linear model, predict the cost of insurance in 2030
For t=2030=2030-1999=31 years
substitute
P=250(31)+2,196
P=$9,946
Part c
According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute in the linear model
12,000=250t+2,196
250t=12,000-2,196
250t=9,804
t=39 years
therefore
1999+39=year 2038
Part d
Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of
P0 and d to the nearest dollar
using a regression calculator
the equation is
ŷ = 239.15065X + 2406.39827
y=239x+2,406
Part e
Using the regression model, predict the cost of insurance in 2030
For t=2030-1999=31 years
P=239(31)+2,406
P=$9,815
Part f
According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute
12,000=239x+2,406
239x=12,000-2,406
239x=9,594
t=40 years
year=1999+40=2039
a) Write an equation of a line in point slope form given the slope -2/3 and the point (-3,2). b) Write an equation in slope intercept form through the points (3,-3) and (2,0) c) write an equation based on this model. Gas cost $4.00 per gallon. If someone paid a startup fee of 5.00, write an equation in slope intercept form based on this model in y = mx+b
Answer:
[tex]y-2\text{ = -}\frac{2}{3}(x+3)[/tex]Explanation:
Here, we want to write the equation of a line in point-slope form
Mathematically, we have that as:
[tex]y-y_1=m(x-x_1)[/tex]where m, which is the slope is -2/3 and (x1,y1) which is the point is (-3,2)
Substituting the values, we have it that:
[tex]y-2\text{ = -}\frac{2}{3}(x+3)[/tex]Karina is baking bread. she buys a small bag of flour that contains 2 2/3 cups of flour. the recipe calls for 2 5/7 cups of flour. does she have enough flour to bake the bread? explain how she can compare the fractions to know for sure.
Using approximation, the two are the same and she contains enough flour.
What is meant by the unitary method?The unitary technique entails finding the value by multiplying the single value and then solving the problem using the initial value of a single unit. If an event may take place in m different ways and a second event can take place in n different ways after it, then the two events that follow can take place in m n different ways.
Given that Karina buys a small bag of flour that has 2 2/3 cups of flour. The recipe calls for 2 5/7 cups of flour.
1) 2 2/3 cups of flour.
= ((2 × 3)+2)/3
= 2.666
Therefore, she get 2.666
2) 2 5/7 cups of flour.
= ((2 × 7) + 5)/7
= 2.714
Therefore, she get 2.714
Using approximation, the two are the same and she has enough flour.
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A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
If a bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. The height of the 7th bounce of the ball is 0.7.
Determining the height of the ballGiven data:
First bounce = 3.75 feet
Successive bounce = 79% or 0.79%
Bounce = 7
Now let determine the height of thee 7th bounce of the ball using this formula
Height = First bounce × (Successive bounce) ^ Number of bounce
Let plug in the formula
Height = 3.75 × (0.79 ) ^7
Height = 0.7
Therefore the height is 0.7.
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Find the distance between points M(6,16) and Z(−1,14) to the nearest tenth.
Answer:
7.3units
Step-by-step explanation:
[tex] \sqrt{(x2 - x1) {}^{2} + (y2 -y1) {}^{2} } [/tex]
[tex] \sqrt{ (- 1 - 6) { \\ }^{2} + (14 - 16) {}^{2} } [/tex]
[tex] = 7.3[/tex]
explain how you got it please
The simplest form of the expression as we have it is; (-4x^4z^2)(2xy^3z^2)
What does it mean to simplify?When we are asked to simplify, what we are asked to do is to write the expression that we have in a form that is simplest. That is, we should put the expression in a form that there would not be any simpler presentation of the expression.
We have;
(-2x^2z)^2(2xy^3z^2)
Then we now have to deal with the exponent outside the bracket;
(-4x^4z^2)(2xy^3z^2)
Thus, we now have the expression in the simplest form that it can take and it can not be further broken down.
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The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
What is statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
In the given statements
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statement "The range of the distribution is around 60 cm" is true.
The range is the spread of your data from the lowest to the highest value in the distribution.
In the given graph
Range=200-140
=60
So it is true.
The center of the distribution is around 180 cm is also true.
Hence the statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
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The following question has two parts. First, answer part A. Then, answer part B.
Use the model to answer the questions.
A rectangle is divided into two sections by a vertical line. The left section is labeled inside with 260. The right section is labeled inside with B. The left edge of the rectangle is labeled 13. Across the top outside of the rectangle, the sections are labeled A tens, a plus sign above the vertical line, and C.
Part A
Carter wants to use the model above to solve 273÷13. Explain how he would find parts A, B, and C of the model.
Part B
The final quotient for 273÷13 is
The knowledge of place value helped in solving 273÷13 with a rectangular model developed by Carter
The part labelled A is 26 tens
The part labelled B is 13 units
The part labelled C is 13 ones
How to determine parts A, B, and C using rectangular model developed by Carterinformation given in the question
A rectangle is divided into two sections by a vertical line
The left section is labeled inside with 260
The left edge of the rectangle is labeled 13
other information is in the attached diagram
How to used the model
Carter's model is a rectangle of length 273 and breadth 13.
273 / 13 = 21
This means that dividing the length into 13 places each unit is 13
273 - 13 = 260
hence the 260 represents 20 units, since one unit is subtracted
The knowledge of place value help to get the numbers to be arranged in tens and ones
putting the numbers in tens is done by dividing by 10
= 260 / 10
= 26
hence, A in tens is equivalent to 26
putting the numbers in ones is dine by dividing by 1
C = 13 / 1
C = 13 ones
a unit is 13, B = 13
B covers same space as C so they are equal
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