HELP!!!!!!!
they are 10 to 10. my screen isn't big enough to screenshot it.
A B C or D
Answers
The points (0, 4) , (1, 2) and (2, 0) are shown in figure.
Option 2 is true.
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
In the table,
The values of x = 0 , 1 , 2
The values of y = 4 , 2 , 0
Now,
The coordinates are;
(x , y) = (0, 4) , (1, 2) and (2, 0)
Here, For the value of x shows the coordinates for x - axis.
The value of y shows the coordinates for y - axis.
So, The points (0, 4) , (1, 2) and (2, 0) are draw on the graph as given in figure.
Thus, The points (0, 4) , (1, 2) and (2, 0) are shown in figure.
Option 2 is true.
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Related Questions
/ Week 1 / Week 1 Monday - Daily Quiz
A rectangle is 5 feet long and 12 feet wide.
What is it's area?
Answers
60 feet² is the area of rectangle.
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.The four sides of a laptop are equal in length and have opposite sides that are parallel to one another.length = 5 feet
wide = 12 feet
area of rectangle = length × width
= 5 × 12
= 60 feet²
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In a rectangle the base measures (x + 7), height (x + 2), area = 36 cm
Calculate perimeter, height and base.
Answers
The values are given as;
Perimeter = 26cm
Height = 4cm
Base = 9cm
How to determine the valueThe formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleNow, substitute the values into the formula, we have;
36 = (x +7)(x + 2)
Now, expand the bracket
36 = x^2 + 2x + 7x + 14
collect like terms
36 = x^2 + 9x + 14
Make into quadratic equation
x^2 + 9x + 14 -36 = 0
x^2 + 9x - 22 = 0
Factorize the equation
x^2 + 11x - 2x - 22 = 0
Factorize further
x(x + 11) - 2( x + 11) = 0
Then, x - 2 = 0, x = 2
or x + 11 = 0
x = -11
Height = x + 2 = 4cm
Base = x + 7 = 9cm
The formula for perimeter is expressed as;
Perimeter = 2( l +w )
Perimeter = 2( 4 + 9)
Perimeter = 2(13)
Perimeter = 26 cm
Hence, the values are 26cm, 4cm and 9cm respectively.
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A cellphone company offers two talk and text plans. The company charges a monthly service fee of $20 for either plan the customer chooses: Customers that choose Talk and Text Plan A are charged five cents a minute and twenty dollars for 250 texts. Customers that choose Talk and Text Plan B are charged ten cents a minute (first 100 minutes free) and fifteen dollars for 200 texts. The equation c = .10(m – 100) + 15 + 20 can be used to represent how much a customer would spend monthly for the minutes used. ** Express Plan A as an equation where c equals the cost and m equals the minutes used. a. Graph each Talk and Text plan to determine when both plans cost the same.
Answers
For question a), we have to write the equation of the cost (c) as a function of the minutes (m), so:
[tex]c_A=0.05\cdot m+20+20[/tex]In the equation above the term 0.05*m represent the 5 cents for minute then we have to sum the $20 for 250 texts and $20 of service fee.
Before we draw the lines, we can solve the question c). If a customer wants to spend $75 monthly we can recommen him the plan wich more minutes for that cost, so we need to calculate the minutes for each plan:
[tex]\begin{gathered} \text{For Plan A:} \\ c_A=75=0.05\cdot m+20+20 \\ 0.05\cdot m=75-20-20=35 \\ m=\frac{35}{0.05}=700 \\ \text{For Plan B:} \\ c_B=75=0.1\cdot(m-100)+15+20 \\ 0.1\cdot(m-100)=75-15-20=40 \\ m-100=\frac{40}{0.1}=400 \\ m=400+100=500 \end{gathered}[/tex]The customer should choose the Plan A, because it has more minutes and more texts for $75.
For point b), we can evaluate each equation in two differents m-values and found the pairs (m, c) to graph the lines, so:
[tex]\begin{gathered} \text{For Plan A, we can choose m=100 and m=500}\colon \\ m=100\Rightarrow c_{}=0.05\cdot100+20+20=45 \\ m=500\Rightarrow c=0.05\cdot500+20+20=65 \\ P_{1A}=(100,45),P_{2A}=(500,65) \end{gathered}[/tex][tex]\begin{gathered} \text{For Plan B, we can choose m=100 and m=500:} \\ m=100\Rightarrow c=0.1\cdot(100-100)+15+20=35 \\ m=500\Rightarrow c=0.1\cdot(500-100)+15+20=75 \\ P_{1B}=(100,35),P_{2B}=(500,75) \end{gathered}[/tex]And the graphs are:
In the Graphs we can see the lines intercept in m=300 and evluating the equations in that value the cost is $55.
whats the middle of 130 - 170
Answers
Answer:
middle number is 150
Step-by-step explanation:
the middle of 130 - 170:
170 - 130 = 40
40/2 = 20
so the middle is:
130 + 20 = 150
or can be found:
170 - 20 = 150
middle number is 150
Answer:
150
Step-by-step explanation:
Add the two extreme numbers and take the average
130 + 170 = 300
300/2 = 150
150 is 20 distant from 130 and also 20 distant from 170
(a)does the figure have reflectional symmetry? if so, give the n-fold number of the symmetry. (b)does the figure have rotational symmetry? if so, give the order and angle measure of the rotation.
Answers
(b) A figure is said to have an n-fold rotational symmetry if rotating through an angle of 360° / n does not change the figure.
In the case of the given figure, rotation through 180° does not change the figure.
Therefore,
[tex]\frac{360^o}{n}=\frac{180^o}{1}[/tex]Cross-multiplying, we have
[tex]\begin{gathered} 180^on=360^o \\ \text{ Dividing both sides by 180, we have} \\ n=\frac{360^o}{180^o}=2 \end{gathered}[/tex]Hence, the order of rotation is 2 and the angle is 180°
Kylie wants to ride her bicycle 27.5 miles this week. She has already ridden 9 miles. If she rides for 5 more days, which equation or tape diagram could be used to represent the context if mm represents the average number of miles she would have to ride to meet her goal?
Answers
The equation to represent the context is 9 + 5m = 27.5
How to frame the equation?
Number of miles Kylie wants to ride in a week= 27.5
Number of miles already ridden = 9
Average number of miles to meet her goal = mm
Let average no. of miles in 5 days = 5m
Rewriting as equation,
9 + 5m = 27.5
How to find the average number of miles?
5m = 37.5 -9
5m = 18.5
m = 18.5
[tex]m =\frac{18.5}{5} \\\\m = 3.7 \text{ or } 3\frac{7}{10}[/tex]
Kylie should travel 3.7 miles per day and 18.5 miles in 5 days to meet her goal
What is an equation?
A mathematical statement that has two expressions with equal values separated by the symbol ' = ' is called an equation. The expression on the left and the expression on the right are shown to be equal in reference to one another. The equations are solved to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no equal to sign in the statement and shall be taken into account as an expression.To learn more about equations, refer:
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The figure below is a net for a triangular prism. What is the surface area of the triangular prism, in square feet?
Answers
The figure consists of,
A rectangle with dimension 15 ft by 7 ft.
Two triangles with base b = 7 ft and height h = 5 ft.
A rectangle with dimension 15 ft by 5 ft.
A rectangle with dimension 15 ft by 8.6 ft.
Determine the surface area of triangular prism.
[tex]\begin{gathered} A=15\cdot7+2\cdot\frac{1}{2}\cdot7\cdot5+15\cdot5+8.6\cdot15 \\ =105+35+75+129 \\ =344 \end{gathered}[/tex]So, surface area of triangular prism is 344 square feet.
A candy stand sells lollipops, gumballs, and chocolates. The gumballs cost 5 cents more than the chocolates. The lollipops cost twice as much as the chocolates. A particular handful containing 3 gumballs, 2 lollipops, and 7 chocolates costs $2.11. What is the cost of each item?
Answers
The cost of lollipops, gumballs, chocolate is $ 0.268, $0.184, $0.134
What is an equation?
An equation is a formula that describes the equality between two expressions, by connecting them with the equals sign '='.
Let the cost of lollipops be x
The cost of gumballs be y
and cost of chocolates be z
We are given that the gumballs cost 5 cents more than the chocolates
mathematically this can be written as
[tex]y=z+0.05[/tex]
Similarly,
The lollipops cost twice as much as the chocolates
mathematically this can be written as,
[tex]x=2z[/tex]
Now finally we purchase 3 gumballs, 2 lollipops and 7 chocolates
The equation can be given as,
[tex]3x+2y+7z=2.11[/tex]
Substituting the values of x and y in this equation we get,
[tex]6z+2(z+0.05)+7z=2.11\\6z+2z+0.1+7z=2.11\\15z=2.01\\z=0.134[/tex]
The cost of chocolates is $0.134
The cost of gumballs is $0.184
And the cost of lollipops is $0.268
Hence, The cost of lollipops, gumballs, chocolate is $ 0.268, $0.184, $0.134
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7.) Use the information to prove:
Given: The Diagram
Prove: EC AD
Answers
With the given information, we have proved that EC ≅ AD as corresponding sided of congruent triangles are congruent too.
What is congruent triangles?Both triangles are said to be congruent if the three angles and three sides of one triangle equal the corresponding angles and sides of the other triangle. We can see in the examples PQR and XYZ that PQ = XY, PR = XZ, and QR = YZ, and that P = X, Q = Y, and R = Z. Then, we can state that XYZ and PQR are related.
We have given that that ∠ADB = ∠ECB
And ∠ABC = ∠EBC as they are vertically opposite angles
And given that AB = EB
Thus, Triangle ABC ≅ Triangle EBC
And as ABC ≅ EBC
EC ≅ AD as corresponding sided of congruent triangles are congruent too.
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A car left the warehouse at 3:00 P.M. The car traveled 62 miles by 4:00 P.M. The car continued traveling at the same average speed. How many miles, altogether, did the car travel by 9:45 P.M.? Round the final answer to the nearest whole number.
Answers
From 3 PM to 4 PM = 1 hour
Speed rate = distance / time
Distance = 62 miles
Replacing:
Speed = 62 / 1 = 62 miles per hour
By 9:45 PM
9:45 - 3 PM = 6 hours .45 minutes = 6.75 hours
Distance = Speed x time = 62 x 6.75 = 418.5 miles
K
Find the average rate of change of the function f(x) = 6x from x₁ = 0 to x₂ = 3.
The average rate of change is
(Simplify your answer.)
Answers
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How do you find the average rate of change of
f
(
x
)
=
2
x
2
+
1
on [x,x+h]?
Calculus Derivatives Average Rate of Change Over an Interval
1 Answer
Steve M
Feb 28, 2017
4
x
+
2
h
Explanation:
The average rate of change of a continuous function,
f
(
x
)
, on a closed interval
[
a
,
b
]
is given by
f
(
b
)
−
f
(
a
)
b
−
a
So the average rate of change of the function
f
(
x
)
=
2
x
2
+
1
on
[
x
,
x
+
h
]
is:
A
r
o
c
=
f
(
x
+
h
)
−
f
(
x
)
(
x
+
h
)
−
(
x
)
=
f
(
x
+
h
)
−
f
(
x
)
h
...
.
.
[
1
]
=
2
(
x
+
h
)
2
+
1
−
(
2
x
2
+
1
)
h
=
2
(
x
2
+
2
x
h
+
h
2
)
+
1
−
2
x
2
−
1
h
=
2
x
2
+
4
x
h
+
2
h
2
−
2
x
2
h
=
4
x
h
+
2
h
2
h
=
4
x
+
2
h
Which is the required answer.
Additional Notes:
Note that this question is steered towards deriving the derivative
f
'
(
x
)
from first principles, as the definition of the derivative is:
f
'
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
This is the function we had in [1], so as we take the limit as
h
→
0
we get the derivative
f
'
(
x
)
for any
x
, This:
f
'
(
x
)
=
h
→
0
4
x
+
2
h
=
4
x
this is a example
a car loses value at a rate of $2,500 per year (slope) you purchase a car for $21,000 which equation can be used to find y its value in dollars, x years after it was purchased
Answers
The value decreases at the rate of 2500 means slope of equation is -2500 and present value is 21000 so y intercept for the line is 21000.
Determine the equation for the car value after x years.
[tex]y=-2500x+21000[/tex]So answer is -2500x + 21000.
The table shows the changes in a city's average weekly temperature.
Week Average Temperature (ºF)
1 24.4
2 24.8
5 26.1
8 27.2
15 30.1
24 33.6
The data shows
trend.
Based on the table, we can assume that the city's average weekly temperature in the 26th week will
Answers
The city's average weekly temperature in the 26th week will be between 30.1 and 33.6 degrees be more than 33.6 degrees.
What is mean by linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The regression line shows slope of 0.4 and has y - intercept as 24.029.
Now,
Since, The slope is positive, we find that when week increase temperature as;
The regression equation will be;
y = 24.029 + 0.4x
For week = 26
y = 24.029 + 0.4x
y = 24.029 + 0.4 × 26
y = 24.029 + 10.4
y = 34.429
Which is greater than 33.6.
Thus, The city's average weekly temperature in the 26th week will be between 30.1 and 33.6 degrees be more than 33.6 degrees.
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The complete question is this;
The table shows the changes in a city's average weekly temperature. Week Average Temperature (ºF) 1 24.4 2 24.8 5 26.1 8 27.2 15 30.1 24 33.6. The data shows a positive linear a negative linear an exponential an unrecognizable trend. Based on the table, we can assume that the city's average weekly temperature in the 26th week will be between 30.1 and 33.6 degrees be more than 33.6 degrees be less than 33.6 degrees not change .
Tammy invested $2000 in a fund for 4 years and was paid simple interest. The total interest that she received on the investment was $400. As a percentage, what was the annual interest rate of her investment?
Answers
Answer:
Use this steps to find your answer
6.5 in. 5 in 7.5 in. What is the total surface area of this prism in square inches?
Answers
6.5 in. 5 in 7.5 in. What is the total surface area of this prism in square inches?
we have that
the total surface area of a prism is equal to
SA=2B+Ph
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
Let
L=6.5 in
W=5 in
H=7.5 in
so
B=L*W=(6.5*5)=32.5 in2
P=2(L+W)=2(6.5+5)=23 in
H=7.5 in
therefore
SA=2(32.5)+23(7.5)
SA=237.5 in2
surface area is 237.5 square inchessee the attached figure to better understand the problem
the surface area is the area of its six rectangular faces
so
SA=2(6.5)8(5)+2((5)(7.5)+2(6.5)*(7.5)=237.5 in2
take the square root of both sides of the equation from part B ( n↑2−c↑2=0 ) and write the resulting equation. how can this equation be true, and what does this show about the relationship between the two triangles?
Answers
SOLUTION
From the question and the instructions given,
Since
[tex]\begin{gathered} n^2-c^2=0 \\ square\text{ rooting both sides } \\ \sqrt{n^2}-\sqrt{c^2}=\sqrt{0} \\ square\text{ cancels square root, we have} \\ n-c=0 \end{gathered}[/tex]Thus, the triangles have all sides congruent, since the triangles are congruent.
Hence, this means that triangle 1 is a right triangle.
The amount of time a certain brand of light bulb lasts is normally distributed with a
mean of 1300 hours and a standard deviation of 65 hours. What is the probability
that a randomly chosen light bulb will last between 1390 hours and 1460 hours, to the
nearest thousandth?
Answers
The probability that a randomly chosen light bulb will last between 1390 hours and 1460 hours is 3.1% to the nearest thousandth.
What is Normal Probability Distribution?In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:
[tex]z = x - \mu/ \sigma[/tex]
The Z-score measures how many standard deviations the measure is from the mean.
In a set with mean and standard deviation , the z-score of a measure X is;
Mean of 1300 hours and a standard deviation of 65 hours.
This is the p-value of Z when X = 1460. So
[tex]z = x - \mu/ \sigma[/tex]
z = 1460 - 1300 /65
z = 1.87
Then has a p-value of 0.031.
0.031 = 3.1% is the probability that a randomly chosen light bulb will last between 1390 hours and 1460 hours, to the nearest thousandth.
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John recently joined a bowling team and each night plays three games. During his first two games he scored 112 and 134. What must John score on his last game to ensure his average for that night will be exactly 132?explain pls.
Answers
Let the score in his last game be
[tex]=x[/tex]The average of the three games is given as
[tex]=132[/tex]Step 1: The formula for average is
[tex]\text{average}=\text{ }\frac{\text{sum of the thre}e\text{ scores}}{3}[/tex]Step 2:Substituting the values of the three scores in the formula above, we will have
[tex]\begin{gathered} \text{average}=\text{ }\frac{\text{sum of the thre}e\text{ scores}}{3} \\ \text{average}=\frac{112+134+x}{3}=132 \end{gathered}[/tex]Step 3 : Cross multiply the equation below
[tex]\begin{gathered} \frac{112+134+x}{3}=\frac{132}{1} \\ \frac{246+x}{3}=\frac{132}{1} \\ 246+x=3\times132 \\ 246+x=396 \end{gathered}[/tex]Step 4: Subtract 246 from both sides
[tex]\begin{gathered} 246+x=396 \\ 246-246+x=396-246 \\ x=150 \end{gathered}[/tex]Hence,
John must score a point of 150 to ensure that his average is 132
Therefore,
Final answer = 150
1.5.PS-9Question HelpError Analysis Simplify the expression - 1.8+(-1.2). On the test, when Tom simplified theexpression he got 0.6. What mistake did Tom likely make when he simplified the expression?- 1.8+(-1.2) = 1 (Type an integer or a decimal.)
Answers
Answer:
-3.0
Explanation:
First, we open the bracket and take note that:
[tex]+\times-=-[/tex][tex]\begin{gathered} -1.8+\left(-1.2\right)=-1.8-1.2 \\ =-3.0 \end{gathered}[/tex]Next, we determine Tom's mistake.
[tex]\begin{gathered} 1.8+(-1.2)=1.8-1.2 \\ =0.6 \end{gathered}[/tex]Therefore, the mistake Tom made was that he ignored/forgot the negative sign before 1.8.
Which expression is equivalent to9 30429O-49 20-13O4 301-(-3)O22COIN | ST
Answers
We must find the expression equivalent to:
[tex]\frac{-2\frac{1}{4}}{-\frac{2}{3}}.[/tex](1) The numerator is a mixed fraction, we can write it as a simple fraction:
[tex]\frac{-2\frac{1}{4}}{-\frac{2}{3}}=\frac{-2-\frac{1}{4}}{-\frac{2}{3}}=\frac{-\frac{8}{4}-\frac{1}{4}}{-\frac{2}{3}}=\frac{(-\frac{9}{4})}{(-\frac{2}{3})}.[/tex](2) Finally, we can rewrite the quotient between numerator and denominator using the symbol ÷, we get:
[tex]\frac{-2\frac{1}{4}}{-\frac{2}{3}}=\frac{(-\frac{9}{4})}{(-\frac{2}{3})}=(-\frac{9}{4})\div(-\frac{2}{3}).[/tex]Answer[tex](-\frac{9}{4})\div(-\frac{2}{3})[/tex]1. Provide a summary of the story “The Stone” Summarize the events in the exposition, rising action, climax, falling action, and resolution. Your written response should include 5 complete sentences.
Answer:
pls hurry
Answers
According to the plot synopsis for the novel "The Stone," a young homosexual guy experiences Taipei's nightlife, complete with all of its thrills and heartbreaks, perils, and hopes.
The Story of the Stone, sometimes referred to as "The Dream of the Red Chamber," was one of the finest books in Chinese literature when it was published about 1760. Gao E painstakingly edited and finished Cao Xueqin's majestic saga's fifth chapter, "The Dreamer Awakens," decades later.
The Story of the Stone has several references to or hints at the issue of the difference between what is true and what is untrue. The first volume in a five-volume series on the illustrious Chinese Jia family is titled "The Story of the Stone."
The major storyline chronicles the development of the love triangle between the three main characters—cousins Bao-yu, Dai-yu, and Bao-chai—as they grow up.
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which measurement is closest to the volume of the container in cubic inches
Answers
The volume of a cylinder is given as;
[tex]\begin{gathered} Vol=\pi\times r^2\times h \\ r=3 \\ h=10.5 \\ \text{Vol}=3.14\times3^2\times10.5 \\ Vol=3.14\times9\times10.5 \\ \text{Vol}=296.73in^3 \end{gathered}[/tex]Therefore, from the options provided, the closest to the volume of the container is 296.88 cubic inches.
Option B is the correct answer
May I get help? I seem to keep losing connection
Answers
Answer
Option C is correct.
A = 1, B = 1, C = 0, D = -8, and E = 7
Explanation
The equation of a circle with center (h, k) and a radius of r, is given as
(x - h)² + (y - k)² = r²
This can then be expanded to form the general form of the equation,
Ax² + By² + Cx + Dy + E = 0
For this question, where the center of the circle lies on the y-axis, the coordinates of the center of that circle will be (0, p)
where p is the y-coordinate of the center of the circle.
(x - h)² + (y - k)² = r²
(h, k) = (0, p)
h = 0, k = p
r = 3 units
(x - 0)² + (y - p)² = 3²
x² + y² - 2py + p² = 9
x² + y² -2py + p² - 9 = 0
Comparing this with Ax² + By² + Cx + Dy + E = 0
A = 1
B = 1
C = 0
D = -2p
E = p² - 9
We can easily see that only Option C has C = 0 and matches the equation of the circle described in the question.
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The volumes, in ml, of olive oil can be modeled by a normal distribution, with mean 508 mL and standard deviation 12 ml.. a. Find the probability that a randomly selected bottle has a volume less than 500 mL. Round your answer to 3 significant figures. b. The probability that a randomly selected bottle has a volume greater than v mL is 0.366. Find the value of v.
Answers
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
Explain the normal distribution with an example?
One straightforward example of anything that has a normal distribution pattern is height: The majority of people are normal height, although there are nearly equal numbers of people who are taller or shorter than average and a very small (but roughly comparable) number who are either extraordinarily tall or extremely short.
The four properties of a normal distribution are visible here. The mean, median, and mode are all equal in normal distributions, which are symmetric, unimodal, and asymptotically distributed.
Add the mean to the x value in step 1. Subtract the difference from the standard deviation in step two. A value of 1380 has a z-score of 1.53. Thus, 1380 is 1.53 standard deviations away from the distribution's mean.
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Look at the following equation:
12,400 × [] = 1,240
What number should go in the box to make the equation true? (1 point)
1/10
1/100
10
100
Answers
A motorcyclist starts his trip at noon and drives 10 miles in the first hour, and then in
each hour after that, he drives 6 more miles than in the previous hour.
After how many hours of driving will the motorcyclist drive a total of 248 miles?
Answers
After 248 miles, the motorcycle rider would have put in 40.6 hours of driving.
By using the arithmetic progression formula, we may find the answer to this problem.
The definition of arithmetic progressionA series of numbers in order known as an arithmetic progression has a constant value as the difference between any two consecutive numbers.
According to what we've been told, the first hour is separated by an arithmetic difference of six miles, or 10 miles. He covered a distance of 248 miles, according to the information we have. It follows that
An = a + (n-1)d, where
An = 248
a = 10
n = ?
d = 6
applying the formula, we have
248 = 10 + (n - 1)6
248 = 10 + 6n - 6
248 = 6n + 4
6n = 248 - 4
6n = 244
n = 244/6
n = 40.6 hours
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Decay (calculus problem)
Answers
Answer:
Step-by-step explanation:
If the half-life is k days, then you have
(1/2)^(300/k) = 0.696
k = 573.788
makes sense, since 69.6% is greater than 50%
Now solve for t in
(1/2)^(t/573.788) = 1/3
t = 909.432 days
makes sense -- about 1.5 half-lives
pleae help me and show work you will be braineist
Answers
The equation of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]where (x1,y1) is a point on the line and m is the slope. To find the slope of a line we use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, we have:
[tex]m=\frac{4-3}{5-(-2)}=\frac{1}{5+2}=\frac{1}{7}[/tex]Then, the equation of the line is:
[tex]\begin{gathered} y-4=\frac{1}{7}(x-5) \\ 7y-28=x-5 \\ x-7y=-23 \end{gathered}[/tex]Therefore:
[tex]x-7y=-23[/tex]The diameter D of a sphere is 13.6 mm calculate thr sphere volume Vuse the value 3.14 for pie, and around to the nearest 10th
Answers
Step 1
State the volume of a sphere
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ \pi=3.14 \\ \frac{Diameter}{2}=\text{radius}=\frac{13.6}{2}=6.8\operatorname{mm} \end{gathered}[/tex]Step 2
Find the volume of the sphere by substitution of values.
[tex]\begin{gathered} v=\frac{4}{3}\times3.14\times(6.8)^3 \\ v=\frac{4}{3}\times3.14\times314.432 \\ v=1316.421973\operatorname{mm} \\ v\approx1316.4\operatorname{mm}^3\text{ to the nearest tenth} \end{gathered}[/tex]Hence, the volume of the sphere= 1316.4mm³ to the nearest tenth
Find the value of X and each arc measurex =mAD=mBC = mDC =mDBC=
Answers
The value of x can be calculated as,
[tex]\begin{gathered} \text{ summation of angles = 360}^{\circ} \\ 12x+90+(2x+5)+(17x-14)=\text{ 360}^{\circ} \\ 31x+95-14=360 \\ 31x=360-81 \\ 31x=279^{\circ} \\ x=\frac{279^{\circ}}{31} \\ x=9 \end{gathered}[/tex][tex]\begin{gathered} \text{mAD }=\text{ 12x} \\ =12\times9 \\ =108^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \text{mBC}=(2x+5)^{\circ} \\ =(2\times9)+5 \\ =18+5 \\ =23^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \text{mDC }=(17x-14)^{\circ} \\ =(17\times9)-14 \\ =153-14 \\ =139^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \text{mDBC }=\text{ }(2x+5)^{\circ}+(17x-14^{})^{\circ} \\ =23^{\circ}+139^{\circ} \\ =162^{\circ} \end{gathered}[/tex]