An irrigation canal is 10 kilometers long and 2 meters deep. It is 4 meters wide at the 2 meters wide at the bottom. How many cubic meters of earth were excavated to make the canal?
The cross section of the canal will form a trapezoid. First, find the area of the cross section. The area of a trapezoid is defined as
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{a+b}{2}h \\ \\ \text{Given} \\ h=2\text{ meters (2 meters deep)} \\ a=4\text{ meters (4 meters wide)} \\ b=2\text{ meters (2 meters wide at the bottom)} \end{gathered}[/tex]Substitute the following values and we get the area
[tex]\begin{gathered} A=\frac{a+b}{2}h \\ A=\frac{4+2}{2}(2) \\ A=\frac{6}{2}(2) \\ A=6\text{ m}^2 \end{gathered}[/tex]Now that we have the area of the cross section, multiply it to the length of the irrigation canal.
[tex]\begin{gathered} \text{Before multiplying, all units must be the same, convert km to meters} \\ 10\operatorname{km}\rightarrow10,000\text{ meters} \\ 6\text{ m}^2\times10000\text{ meters} \\ \Longrightarrow60000\text{ m}^3 \end{gathered}[/tex]Therefore, they have to excavate 60,000 cubic meters of earth to make the canal.
Suppose you pay only the interest on a loan. Will the loan ever be paid off? Why or why not? I have no idea if this is correct
No. if only the interest is paid, the principal never decreases
The number of people in thousands who own a cell phone is a function of the time in years starting in 1990 where p(t) = 20(1.075)^tGrowth or Decay?What is the initial amount of people who own cell phones?Determine the growth/decay rate.
Solution
[tex]\begin{gathered} 1)\text{ Answer, This is GROWTH } \\ 2)\text{ The initial amount of people wo own a cell phone is },\text{ means when t = 0} \\ P(t)=20(1.075)^t \\ p(t)\text{ = }20(1.075)^0 \\ p(t)\text{ = 20 }\times\text{ 1} \\ p(t)\text{ = 20} \end{gathered}[/tex][tex]\begin{gathered} 3)\text{ To }\det er\min e\text{ the growth/decay rate, we have} \\ p(t)=20(1.075)^t \\ p(t)=20(1+0.75)^t \\ \text{Answer, growth rate is: 0.75 =0.75\%} \\ \end{gathered}[/tex]Write an equation in point-slope form for the line that passes through the given points.
(-4,7). (6.3)
Answer:
[tex]y=-\frac{2}{5}x+5.4[/tex]
Step-by-step explanation:
Step 1: plot points
Step 2: find the RISE/RUN (-4/10 or -2/5)
Step 3: find where it intersects the y axis (5.4)
y=mx+b where x and y are varables, m is the slope, and b is the y-int
[tex]y=-\frac{2}{5}x+5.4[/tex]
Hope that helps
A+(b+c)=(a+b)+c what property is this? The options are as follows
Identity property of multiplication
Associative property of multiplication
Identity prop. Of addition
Multiplicative inverse prop.
Additive inverse prop.
Commutative prop of addition
Commutative prop of multiplication
Transitive property
Properties
Given:
The properties and their notations are given.
To match:
Explanation:
31. It is given that,
[tex]a+0=a[/tex]Since zero is the additive identity.
So, the property is an identity property of addition.
32. It is given that,
[tex]a+b=b+a[/tex]Here, the property is the commutative property of addition.
33. It is given that,
[tex]a\cdot(b\cdot c)=(a\cdot b)\cdot c[/tex]Here, the property is an Associative property of multiplication.
34. It is given that,
[tex]a+(-a)=0[/tex]Since -a is the additive inverse of a.
So, the property is the Inverse property of addition.
35. It is given that,
[tex]a\cdot1=a[/tex]Since 1 is the multiplicative identity.
So, the property is an identity property of multiplication.
36. It is given that,
[tex]a\cdot(b+c)=ab+ac[/tex]Here, the property is a distributive property of addition.
37. It is given that,
[tex]a\cdot b=b\cdot a[/tex]Here, the property is a commutative property of multiplication.
38. It is given that,
[tex]a\cdot\frac{1}{a}=1[/tex]Here, the property is an inverse property of multiplication.
39. It is given that,
[tex]a+(b+c)=(a+b)+c[/tex]Here, the property is an Associative property of addition.
Final answer:
31. E
32. A
33. D
34. AC
35. AB
36.
180/9 as a whole number
Answer:
20
Step-by-step explanation:
180 ÷ 9 = 20
Find the value of x and the length of ST
x = 13
The length of ST is 78
Explanation:ST and SR are tangents
From the diagram
ST = 9x - 39
SR = 6x
Note that:
Two tangents drawn from the same point external to a circle are equal
That is, ST = SR
9x - 39 = 6x
9x - 6x = 39
3x = 39
x = 39/3
x = 13
ST = 9x - 39
Suubstitute x = 13
ST = 9(13) - 39
ST = 117 - 39
ST = 78
7. Write the slope-intercept form of the equation of the line through the given point with the given slope. Write answer as y=mx+b. through: (-1, 1), slope = -6 Vour answer
Answer:
y = -6x - 5
Explanation:
The equation of a line with slope m that passes through the point (x1, y1) can be calculated using the following equation:
[tex]y-y_1=m(x-x_1)[/tex]So, replacing (x1, y1) by (-1, 1) and m by -6, we get:
[tex]\begin{gathered} y-1=-6(x-(-1)) \\ y-1=-6(x+1) \end{gathered}[/tex]Now, to write the answer as y = mx + b, we need to solve the equation for y, so we get:
[tex]\begin{gathered} y-1=-6(x)-6(1) \\ y-1=-6x-6 \\ y-1+1=-6x-6+1 \\ y=-6x-5 \end{gathered}[/tex]Therefore, the answer is y = -6x - 5
what is the product of 24.154 and 0.18
Answer:
4.34772
4.3 with the correct amount of sig figs but you don't really have to worry about that unless you've talked about it in class
Step-by-step explanation:
the product of two numbers is the result of those two numbers being multiplied. So, 24.154 * 0.18 = 4.34772
The value of a in y = ax²+bx+c and the vertex of the parabola are given. How many x-intercepts does the parabola have? Explain how you arrived at this number.a=1; vertex at (2,0)The parabola has x-intercept(s), because the parabola opensand the vertex isthe x-axis.
Given: The value of 'a' in y = ax²+bx+c is a=2 and vertex is at (2,0).
Required: To find the x-intercepts.
Explanation: The x-coordinate of the vertex is 2. Also, we know that x-coordinate is given by
[tex]x=-\frac{b}{2a}[/tex]Hence, putting the value of x=2 and a=1 we get
[tex]\begin{gathered} 2=-\frac{b}{2(1)} \\ b=-4 \end{gathered}[/tex]Now putting y=0, x=2, a=1, and b=-4 in eq of parabola we get
[tex]\begin{gathered} 0=2^2-4(2)+c \\ c=4 \end{gathered}[/tex]Now the equation of the parabola is,
[tex]y=x^2-4x+4[/tex]Now to find x-intercepts put y=0 i.e.,
[tex]\begin{gathered} x^2-4x+4=0 \\ (x-2)^2=0 \\ x=2,2 \end{gathered}[/tex]Hence there is only one x-intercept at (2,0). The opening of the parabola can be seen in the graph below-
Final Answer: The parabola has one x-intercept because the parabola opens upward and the vertex is on the x-axis.
Help please!
I can’t find the probability of a pretty girl telling me the answer to what 2x2 is
May I ask you, pretty girl, what is it?
Answer: depends how often you meet someone
Step-by-step explanation: You can multiply 2 times 2 and if you know the answer to that multiply that times the number of times u meet someone and divide by 2.
Find the value of X in the length of VR
Since V is between R and T, then:
[tex]RT=VR+VT\text{.}[/tex]Substituting VR=3x, VT=5x+9, RT=33, and solving for x we get:
[tex]\begin{gathered} 33=3x+5x+9, \\ 33=8x+9, \\ 33-9=8x, \\ 8x=24, \\ x=3. \end{gathered}[/tex]Substituting x=3 in VR we get:
[tex]\text{VR}=3\cdot3=9.[/tex]Answer:
The value of x is 3.
The length of VR is 9.
Sean and Darryl are racing on a track. Sean runs 6 miles per hour and gets a 0.25 mile head start. Darryl runs 0.7 mile per hour faster than Sean. If Darryl and Sean run the same distance, how many hours, x, do they run? 6x + 0.25 = 0.7x 0 6x - 0.25 = 3.7x 0 6x +0.25 = 6.7x D 6x + 0.25 = 4.7x
The relation between speed, distance and time is express as :
[tex]\text{ Sp}eed\text{ =}\frac{Dis\tan ce}{Time}[/tex]Sean and Darryl are racing on a track.
Sean runs 6 miles per hour and gets a 0.25 mile head start.
Speed of Sean = 6
x is the time taken by Sean
So, Distance = speed x Time
Distance travel by sean = 6x
Since, Sean gets a 0.25 mile head start.
So, total distance travel = 6x + 0.25
Darryl runs 0.7 mile per hour faster than Sean,
Speed of darryl = 0.7 + Speed of sean
Speed of daryl = 0.7 + 6
Speed of darryl = 6.7 miles per hour
x is the time taken by Darryl
So, Distance = Speed x Time
Distance = 6.7x
Distance travel by Darryl = 6.7x
Since distance travel by darryl and sean is equal so,
6x + 0.25 = 6.7x
Answer : C) 6x + 0.25 = 6.7x
Need help please. ASAP
(2y - 1)/ -3 = -5 , prove y = 8: Hence proved
5n - 42 = 12n, prove n = -6: Hence proved
2x + 30 = -4(5x -2), prove x = -1 : Hence proved
18x - 2(3x + 1) = 5x -16, prove x = -2 : Hence proved
What is Algebra?
One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.
1) (2y - 1)/ -3 = -5
Solving for y
(2y - 1)/ -3 = -5
multiply both side with -3
(2y - 1) x (-3)/(-3) = (-5)(-3)
2y - 1 = 15
adding 1 both side
2y - 1 + 1 = 15 + 1
2y = 16
dividing 2 both side
2y / 2 = 16 / 2
y = 8
Hence Proved
2) 5n - 42 = 12n
Solving for n
5n - 42 = 12n
adding 42 both side
5n - 42 + 42 = 12n + 42
5n = 12n + 42
adding -12n both side
5n - 12n = 12n - 12n + 42
-7n = 42
dividing -7 both side
-7n/-7 = 42/ -7
n = -6
Hence proved
3) 2x + 30 = -4(5x -2)
solving for x
first simplify -4(5x -2)
2x + 30 = -20x + 8
adding 20x both side
2x + 20x + 30 = -20x + 20x + 8
22x + 30 = 8
adding -30 both side
22x + 30 - 30 = 8 - 30
22x = -22
dividing 22 both side
22x / 22 = -22/22
x = -1
Hence proved
4) 18x - 2(3x + 1) = 5x -16
solving for x
first simplify - 2(3x + 1)
18x - 6x - 2 = 5x - 16
adding -5x both side
18x - 5x - 6x - 2 = 5x - 5x - 16
13x - 6x - 2 = -16
7x - 2 = -16
adding 2 both side
7x - 2 + 2 = -16 + 2
7x = -14
dividing 7 both side
7x/ 7 = -14 / 7
x = -2
Hence proved
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Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
The number of students who chose not to take French their freshman year is 147.
According to the question,
We have the following information:
72% of students chose to study French their freshman year.
Now, 72% of students is equal to 378.
Let's take the number of students to be x.
So, we have:
72x/100 = 378
72x = 378*100
x = (378*100)/72
x = 525
Now, we have to find the number of students who chose not to take French their freshman year:
(100%-72%)
28%
Now, we have to find the 28% of total number of students:
(28*525)/100
14700/100
147
Hence, the number of students who chose not to take French their freshman year is 147.
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rewrite using a single positive exponent (4^-3)^7
The given expression is
(4^-3)^7
We would apply the law of exponents which is expressed as
(a^- b) = 1/a^b
We can see that
a = 4
b = - 3
Writing it using a single positive exponent, it becomes
4^ - 3 = 1/4^3 = 1/64
The final expression would be
(1/64)^7
A-) who won the race? a1)By how many yards of difference? B-) How many yards behind the starting line does Yolanda have to leave for the race to end in a draw?
EXPLANATION
Let's see the facts:
Race = 100-yard
Toko--> 10 yards < Yolanda
Second part:
Yolanda --> 10 yards behind the starting line
If each geil ran at the same speed as the first race, the appropiate relationship is as follows:
Yolanda's speed = 100 yards/race
Yoko's speed = 90 yards/race
Distance= ratex time
For the second race, Yolanda ran 110 yards at the same speed --> So it will take 110/100 = 1.1 times to finish the race.
Yoko runs 100 yards at the same speed so it will take her 100/90= 1.11111... times to finish the run.
As 1.11 is less time than 1.1111, Yolanda will win the race.
b) In order to finish in a tie, the times must be the same.
Let x be the head start given to Yoko so that they tie.
time = distance / rate
[tex]\frac{100+x}{100}=\frac{100}{90}[/tex]Multiplying both sides by 100:
[tex]100+x=100\cdot\frac{100}{90}[/tex]Subtracting -100 to both sides:
[tex]x=100\cdot\frac{100}{90}-100[/tex]Simplifying:
[tex]x=111.11111\ldots-100=11.111\ldots[/tex]So, if Yoko has 11.111... head start, they should tie on the next race.
Instructions for a chemical procedure state to mix salt, baking soda, and water in a 22 : 14 : 5 ratio by mass. How many grams of baking soda would be required to make a mixture that contains 55 grams of salt?
35 grams of baking soda will be required for the mixture
The ratio of mix salt to baking soda to water = 22:14:5
Let x be the total quantity of the mixture
A mixture is a substance composed of two or more unrelated chemical components. A physical blending of two or more substances that maintains their own identities takes the form of solutions, suspensions, or colloids.
Now the sum of the ratio is 22+14+5 = 41
So, 55 grams of salt = 22/41x
Solving for x we get:
x = 55*41/22
x = 102.5 grams
The total quantity of the mixture is 102.5 grams
Quantity of baking soda required = 14/41 of 102.5
= 14/41*102.5
= 35 grams
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Is w = 12 a solution to the inequality below?
Answer:
No
Step-by-step explanation:
No, it is not a solution. You can find this answer by plugging in 12 for 2 for w.
0>12-132/12
132/12=11
12-11=1
0>1
0 is not greater than 1, so the answer is no.
54 is the product of 3 and Janelle's age
which describes the domain of the figure represented below? ANSWER CHOICES :[8,0)(0,8)[0,8)
We have the following:
The domain is the input values or also the x-axis values.
According to the graph we can see that we go from 0 to 8.
Because the point at 0 is filled, it means that it includes the number and that means that it is a closed interval [].
On the contrary, at point 8, the point is hollow, it means that it reaches 8, but it does not include the number 8, which means that it is an open interval ().
Which means that the correct answer is:
[0, 8)
The table shows the linear relationship between the balance of a student's savings account and the number of weeks he has been saving Savings Account Week 0 1 13 Balance (dollars) 123 Based on the table, what was the rate of change of the balance of the student savings account in dollars and cents per week?
7 dollars per week
Explanation:Rate of change = change in balance (dollars)/change in weeks
for (0, 32) and (1, 39)
Rate of change = (39 - 32)/(1 - 0)
Rate of change = 7/1 = 7
For (1, 39) and (3, 53)
Rate of change = (53 - 39)/(3 - 1)
Rate of change = 14/2
Rate of change = 7
Since the rate of change is constant from calculation, then the rate of change of the balance of the student savings account in dollars and cents per week is 7 dollars per week
Can a table with same input and output be a function like in the picture:
Yes, because each value of x still corresponds to only one value of y.
can somebody please help me with this question
in a classroom challenge,students had to create a triangular pyramid using various items. Each group then use your measurements to remind the volume . which group found the volume of triangle pyramid with a base area of 16 square in?
Volume of a triangular pyramid = 1/3 × base area × height
We have been given base area as 16 square in
Volume of a triangular pyramid = 1/3 × 16 × height
We need to check the options for the expression whose result will give a base area of 16 square in.
From the options:
(8×3)/2 = 12
(11×4)/2 = 22
(16 ×18)/2 = 144
(8 × 4)/2 = 16
1/3 and the height is common to all options. The expression in bracket represent the base area.
Hence, the group that found the volume of triangle pyramid with a base area of 16 square in is
[tex]\frac{1}{3}(\frac{8 ×4}{2})\times q\text{ (option D)}[/tex]Find the probability of selecting a 10 or diamond when a card is drawn from a standard deck of cards.
The probability of selecting a 10 or Diamond when a card is drawn from a standard deck of cards is: 17/52
The question asks us to find the probability of picking a 10 or diamond from a deck of cards.
A standard deck of cards contains 52 cards in total.
The deck contains 4 "10s"
And the deck also contains 13 diamond cards.
Thus, we can find the probability of drawing a "10" as:
[tex]P(10)=\frac{n\text{umber of 10s}}{total\text{ number of cards in deck}}=\frac{4}{52}[/tex]Similarly, we can find the probability of drawing a diamond as:
[tex]P(\text{diamond)}=\frac{n\text{umber of diamonds}}{total\text{ number of cards in deck}}=\frac{13}{52}[/tex]Now that we have the individual probabilities, we can find the probability of drawing a 10 or a diamond using the OR probability:
[tex]\begin{gathered} P(A\text{ OR B)= P(A) + P(B)} \\ \text{where, A and B are independent events} \end{gathered}[/tex]Therefore, we can solve the question. This is done below:
[tex]\begin{gathered} \text{Probability of selecting a 10 or a diamond P(10 OR Diamond)=} \\ P(10)+P(\text{Diamond)} \\ \\ \text{But P(10)=}\frac{4}{52} \\ P(\text{Diamond)}=\frac{13}{52} \\ \\ \therefore P(10\text{ OR Diamond)=}\frac{4}{52}+\frac{13}{52}=\frac{17}{52} \end{gathered}[/tex]Thus, the probability of selecting a 10 or Diamond when a card is drawn from a standard deck of cards is: 17/52
10. Given: BD || CE25= 26Prove: AC = AE(a) BD ICE(b) AC AE(c) 25* LC; 26 = LE(d) 25 = 26(e) LC= LE6DE
The image contains a figure in which angles and sides are named, some data is given, and the proof is to be provided.
Every proof starts with the given data.
Thus, from the options, we select those containing the information provided:
a) BD is parallel to CE
d) Angle 5 is congruent to angle 6
Now we can see the segments AB and AD have one tick mark. This means they are congruent or have the same measure.
AB is congruent to AD
The triangle ABD, having two equal sides, is isosceles. Every isosceles triangle has two congruent angles, in this case, angles 5 and 6.
Thus, the next step in the proof is:
c) Angle 5 is congruent to C and angle 6 is congruent to E
Because of the transitive property of congruence, it follows:
e) Angles C and D are congruent
Being two angles in a triangle congruent, it follows the triangle is isosceles, thus:
b) AC and AE are congruent
This is the final step of the proof
Which property is shown -2x1/-2=1
Answer: The answer is Multiplicative Inverse.
Step-by-step explanation: I hope this helps.
Can someone solve this equation using the quadratic formula and simplifying in radical form if needed
For a quadratic equation of the form:
[tex]av^2+bv+c=0[/tex]The quadratic formula is:
[tex]v_{1,2}=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]In this case, we have the eqaution:
[tex]11v^2+8v=4[/tex]First, let's rest 4 on both sides to get 0 in the right hand side:
[tex]11v^2+8v-4=0[/tex]Then we can use the quadratic formula:
[tex]v_{1,2}=\frac{-8\pm\sqrt[]{8^2-4\cdot11\cdot(-4)}}{2\cdot11}[/tex]And solve:
[tex]\begin{gathered} v_{1,2}=\frac{-8\pm\sqrt[]{64^{}+176}}{22} \\ v_{1,2}=\frac{-8\pm\sqrt[]{240}}{22} \\ v_{1,2}=\frac{-8\pm\sqrt[]{16}\sqrt[]{15}}{22} \\ v_{1,2}=\frac{-8\pm4\sqrt[]{15}}{22} \\ v_{1,2}=\frac{-4\pm2\sqrt[]{15}}{11} \end{gathered}[/tex]Then the two solutions are:
[tex]\begin{gathered} v_1=\frac{-4-2\sqrt[]{15}}{11} \\ v_2=\frac{-4+2\sqrt[]{15}}{11} \end{gathered}[/tex]In anatomy, a student learned that the average resting heart rate is between 60 and 100 beats per minute. The student decided to record the heart rate of people over five minutes while waiting in line at the pharmacy. The dot plot shows the results.
Dot plot with 1 dot at 62, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, and 2 dots at 89
Which statement below best describes the shape of the distribution?
The data is roughly symmetrical distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is not symmetrically distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is skewed left, with fewer values on the left end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The correct option regarding the data-set represented by the dot plot is represented as follows:
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
Dot plotA dot plot shows the number of times that each observation appears in the data-set.
Hence, the complete data-set in this problem is given as follows:
62, 68, 68, 68, 69, 70, 70, 72, 72, 72, 75, 75, 76, 78, 78, 80, 80, 80, 89, 89.
The mean of a data-set is the sum of the observations divided by the number of observations, hence it is given by:
Mean = (62 + 3 x 68 + 69 + 2 x 70 + 3 x 72 + 2 x 75 + 76 + 2 x 78 + 3 x 80 + 2 x 89)/20 = 74.55.
The median is the middle value of the data-set. The data-set has 20 elements, hence the median is the mean of the 10th and the 11th element, given as follows:
Median = (72 + 75)/2 = 73.55.
The mean is greater than the median, hence the data is right skewed and the correct option is given as follows:
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
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Answer: A/The data is roughly symmetrical distributed, with most values clustered from 68 to 80 beats per minute.
Step-by-step explanation: Just got it right on the test