[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$40\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases} \\\\\\ 40 = (500)(\frac{r}{100})(4) \implies 40=20r\implies \cfrac{40}{20}=r\implies \stackrel{\%}{2}=r[/tex]
A ubmarine tart at 0 unit and ha group of 3 float and group of 4 anchor attached. Which expreion would make the ubmarine float the highet? −532−4 53−2−4 −53−2−4 235−4 −23−5−4 23−5−4 What will it final poition be? 34 unit
The following are three equivalent expressions for the submarine's final position -(5)(3) - (2)(4), -(5)(3) + (-2)(4) and -(5)(3) + (2)(-4)
What is defined as the equivalent expressions?
Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value.Each float advances by 5 units.
Each group takes a two-unit step.
As a result, the submarine's final position is:
Final = -(5)(3) - (2)(4)
The minus "-" symbol indicates that the submarine is sinking.
Thus, the following are equivalent expressions for the submarine's final position:
-(5)(3) - (2)(4), -(5)(3) + (-2)(4) and -(5)(3) + (2)(-4)
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A 13 km stretch of road needs repairs. Workers can repair 3 1/2km of road per week.
How many weeks will it take to repair this stretch of road?
The workers would need 3.71 weeks to repair the road.
A generalization of arithmetic in which letters representing numbers are combined using arithmetic rules
Given that the total length of the road is 13km. Workers can repair 3.50 roads per week.
To determine the number of weeks required to repair the road, divide the total by per week. The equation would be:
13 ÷ 3.5
= (13 x 10)/35
= 130/ 35
= 3.71
Therefore the workers would need 3.71 weeks to repair the road.
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3d ÷ (d*d*d/4c) as one fraction
Answer: (3/4c*d*d)
Step-by-step explanation:
First, get rid of the denominator by multiplying the numerator by it.
so d*d*d*4c*.
Then now its 3d/d*d*d*4c, you can eliminate a d from the numerator and denominator, and now it's (3/4c*d*d)
A group of friends were working on a student film that had a budget of $1100. They used 45% of their budget on props. How much money did they spend on props?
A group of friends were working on a student film. The money did they spend on props is $495.
percentage :
a percentage is a number or ratio expressed as a fraction of 100or A percent is one one-hundredth (1/100) of something.It is denoted by % symbol.budget of group working on a student film = $1100
They used percentage of their budget on props. = 45%
then money spend on props is calculated as :
= 45% of 1100
= (45/100) x 1100
= 45 x 11
= $495
A group of friends were working on a student film. The money did they spend on props is $495.
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An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x)=−x2+10x+9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.
The irrigation system is positioned 9.5 feet
The spray reaches a maximum height of 34.5 feet
The spray reaches all the way to the ground at about 10.87 feet
How to find the maximum height of the spray
The standard form of a quadratic equation is given by the formula
y = ax^2 + bx + c
compared with the given equation h(x) = −x^2 + 10x + 9.5 the solutions are calculated as follows
The irrigation position refers to the value of h(x) at x = 0
h(x) = −x^2 + 10x + 9.5
h(0) = 0^2 + 10*0 + 9.5
= 9.5
The maximum height is at the symmetry of the parabolic curve, for a curve opening downward.
At the symmetry x = -b/2a
x = -b/2a = -10/(2 * -1) = 5, At x = 5, then y is
h(5) = −(5)^2 + 10 * 5 + 9.5 = 34.5
The maximum horizontal distance is at one of the roots solved as
h(x) = −x^2 + 10x + 9.5
x = 10.87 OR -0.87
The maximum distance is the greatest distance form the origin (0, 0). Therefore maximum distance is at x = 10.87 feet
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complete question
An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x^2+10x+7.5 where x is the number of feet away from the sprinkler head (along the ground) the spray is.
The irrigation system is positioned____ feet above the ground to start.
The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.
The spray reaches all the way to the ground at about_____ feet away
find the mean of the following group of numbers: 6.1, 5.9, 4.2, 5.9, and 10.7. round your answer to the nearest tenth. responses 4.2 4.2 10.7 10.7 6.6 6.6 6.5
The mean of the given set of group numbers is 6.6
Given,
In the question:
The Group of numbers are as follows:
6.1, 5.9, 4.2, 5.9 and 10.7
To find the mean of the given set of group of numbers.
Now, According to the question:
Given is the following data:
6.1, 5.9, 4.2, 5.9 and 10.7
We can find the mean of the given set of data using the formula-
Mean (M) = Σ a[i]/n = (Sum of all the elements)/(total number of elements)
Now, n = 5
and Σ a[i] = 6.1 + 5.9 + 4.2+ 5.9 + 10.7 = 32.8
Putting the values in the formula, we get:
M = 32.8/5 = 6.56 = 6.6
Hence, The mean of the given set of group numbers is 6.6
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Ana is bowling. She pays $4 per game and $7 to rent shoes. After three games, each additional game is free. Is the total cost to bowl a function of the number of games played? Use a table or graph to help explain your answer.
Answer:
$19.00
Step-by-step explanation:
Write an equation in point-slope form of the line that passes through the point (1, 0) with slope -1/4
Answer:
y = -1/4(x-1)
Step-by-step explanation:
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) From the point given [tex]y_{1}[/tex] = 0 and [tex]x_{1}[/tex] = 1
m = slope -1/4 Plug these in and get
y - 0 = -1/4(x - 1) y-0 is just y
Joseph had 7 1 4 ounces of candy to share with his friends. He gave them 2 4 5 ounces of candy when they came over to play video games. How many ounces of candy does joseph have left?.
Joseph left 469 ounces of candy, according to the given question.
What do you mean by candy?
A sugar-based confection that frequently contains filling and flavoring: a slice of such a confection is called candy. Something that has a lighthearted or frivolous appeal and visual delights.
According to data in the given question,
We have:
Total ounces of candy = 714
Number of candy he shared = 245
Now, we need to determine the candy he has left,
= Total number of candy - Number of shared candy
= 714 - 245
= 469
Therefore, he left 469 ounces of candy.
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Between which two consecutive whole numbers does the length of the diagonal fall?
Which whole number is it closer to? Use the drop-down menus to show your answer.
The length of the diagonal is between 4 and 5.
What is square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The length of the diagonal = √18
Now,
Since, The length of the diagonal = √18
And, √18 = 4.24
Thus, The number 4.24 is lies between two whole numbers 4 and 5 as;
⇒ 4 < 4.24 < 5
⇒ 4 < √18 < 5
⇒ √16 < √18 < √25
Thus, The length of the diagonal is between 4 and 5.
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Given the shape, find the length AD (x)
The length of AD is 8.58 units
Here triangle CDE and triangle CAB are similar triangles.
We know that the corresponding sides of similar triangles are in proportion.
CD/CA = CE / CB = DE/AB
Consider, CD/CA = DE/AB
15/(15 + x) = 7/11
15 * 11 = 7 * (15 + x)
165 = 105 + 7x
7x = 165 - 105
7x = 60
x = 8.58 units
Therefore, the length of AD is 8.58 units
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please help me this is geometry
Answer:
RT
Step-by-step explanation:
Hypotenuse is the greatest and since it is obtuse, it will be even longer.
Answer:
RT is the longest segment.
Step-by-step explanation:
If Angle S is 92°, then AngleR and AngleT are both acute angles. So AngleS is the biggest angle, so the side opposite AngleS is the biggest side. RT is the side opposite from AngleS. RT is the biggest side.
Louis recorded how many times he could jump rope without stopping. Here is
his data:
50 15 102 64 29 55 100 97 48 81 61
Find the median, upper quartile, and lower quartile of his data.
28 divided by x + 4 = 11
Answer:
x= -16/11
Step-by-step explanation:
hope this helps
Answer: x=4
Step-by-step explanation:
28 divided by x+4=11
28 divided by x=7
28/7=4
30.08 rounded nearest 10
Consider the diagram shown. what is the angle of x
By using angles properties (sum of interior angles of a triangle and so) we will see that the measure of angle x is 120°.
How to get the value of angle x?Let's define C as the angle inside the triangle that is adjacent to angle x.
We can see that these two are supplementary angles, then we know that:
C + x = 180°.
We also can see that C is an interior angle of a triangle, and remember that the sum of all interior angles of a triangle is equal to 180°, then we can write
68° + 52° + C = 180°
With that equation, we can find the value of C.
C = 180° - 52° - 68° = 60°
Then.
x + C = 180°
x + 60° = 180°
x = 180° - 60° = 120°
That is the measure of angle x.
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A random sample of 85 printers discovered that 35 of them were being used in small businesses. Find the 99% confidence interval for the population proportion of printers that are used in small businesses
The 99% confidence interval for the population proportion of printers that are used in small businesses, using the z-distribution, is of:
(0.2743, 0.5493)
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the equation presented next:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the point estimate of the parameter.z is the critical value of the z-distribution.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
(the critical value can be found either with the z-table or with a z-distribution calculator).
The sample size and the estimate are listed as follows:
[tex]n = 85, \pi = \frac{35}{85} = 0.4118[/tex]
The lower bound of the interval is obtained as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4118 - 2.575\sqrt{\frac{0.4118(0.5882)}{85}} = 0.2743[/tex]
The upper bound of the interval is obtained as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4118 + 2.575\sqrt{\frac{0.4118(0.5882)}{85}} = 0.5493[/tex]
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I don't know whether this line is a negative or positive. The line is crossing the origin and is in the 1 quadrant and 3 quadrant. Please help!!
The given line is positive.
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
Given that,
The line is crossing the origin and is in the 1 quadrant and 3 quadrant.
This means, the graph of the line starts at the bottom left and goes towards the top right.
If a line has a positive slope, then y always rises when x rises and always falls when x falls (i.e., m > 0). The line's graph thus begins at the bottom left and moves up to the top right.
So, the given line is positive.
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After a shopping trip, the amount of money
Katrina has left can be modeled by the expression
75-9. 5t-11. 75s, where t is the number of t-shirts
and s is the number of pairs of shorts Katrina bought.
a. Describe what each term of the expression
represents in this situation.
b. How many t-shirts and shorts might Katrina have
bought?
Answer:
66
Step-by-step explanation:
I would like to be walked through this and see if my answer is correct as well as how to do it
Answer:
perimeter = 16 ft
Step-by-step explanation:
You want the perimeter of an isosceles triangle with side length 5 ft and altitude 4 ft.
Base lengthThe side lengths being equal mean the triangle is isosceles. That also means altitude PS bisects the peak angle and segment QR. Once we find the length QS using the Pythagorean theorem, we can double that measure to find QR.
The Pythagorean theorem tells us ...
QS² +PS² = QP²
QS² +(4 ft)² = (5 ft)²
QS² = (25 ft²) -(16 ft²) = 9 ft² . . . . . evaluate squares, subtract 16 ft²
QS = √(9 ft²) = 3 ft
Now we know the base length is ...
QR = 2·QS = 2(3 ft) = 6 ft
PerimeterThe perimeter is the sum of the outside edge lengths:
Perimeter = PQ +QR +RP
Perimeter = (5 ft) +(6 ft) +(5 ft) = 16 ft
The perimeter of ∆PQR is 16 feet.
__
Additional comment
With some practice, you can learn to recognize a 3-4-5 right triangle. That is the triangle used here for each of the right triangles that make up ∆PQR. Once you identify the long side as 4 and the hypotenuse as 5, you know immediately the short side is 3.
The set {3, 4, 5} is called a "Pythagorean triple." Other triples commonly seen in high school problems are {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. Legs of these lengths form a right triangle. Knowing any two (or their ratio) tells you immediately the value of the third. Of course, these triples can be scaled by any factor. (3, 4, 5) scaled by 2 is (6, 8, 10), another commonly seen triple.
There are no isosceles right triangles that have integer values for both the legs and the hypotenuse. If the legs are both 4, the hypotenuse will be 4√2 ≈ 5.657... (an irrational number), not 5.
a university found that of its students withdraw without completing the introductory statistics course. assume that students registered for the course. a. compute the probability that or fewer will withdraw (to 4 decimals). 0.2061 b. compute the probability that exactly will withdraw (to 4 decimals). 0.2182 c. compute the probability that more than will withdraw (to 4 decimals). 0.5886 d. compute the expected number of withdrawals.
The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
Compute the probability that 2 or fewer will withdraw,To determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:Then, multiply this quantity by, = 190Which is the number of ways to choose 2 students from the total of 20. Therefore:The probability that exactly 2 students withdraw is Following an process determine that: The probability that exactly 1 student withdraw is The probability that exactly none students withdraw is Finally, the probability that 2 or fewer students will withdraw is,= 0.355Compute the expected number of withdrawals.Hence ,The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.hence,The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
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Write the equation of the line in fully simplified slope-intercept form.
The equation of the straight line in slope-intercept form is given by
y = -x +6 .
The line of the graph is clearly passing through the points (5,1) and (3,3) .
Hence the slope of the line = (3 - 1) / (3 - 5) = 2 / (-2) = -1
The equation of the straight line will be given by the formula:
y-3 = -1 (x-3)
or, y - 3 = -x +3
or, y + x = 6
One of the most popular ways to display a line's equation is in the slope intercept form, which looks like a straight line.
When the slope of anything like the straight line and in fact the y-intercept are known, the slope intercept formula can be used to determine the equation of a line the y-coordinate of the point where the line crosses the y-axis. A line cannot exist unless every point on the line fulfils an equation.
Hence the equation of the line in slope intercept form is y = -x +6
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help me quick pls/....................
Answer:
A
Step-by-step explanation:
First off, "A" is the only one that even has "x cubed minus one" in it. The y squared divided by twenty-four is also present.
what is the smallest number 4.36,4.3,4.06,4.306
Answer: its 4.06
Step-by-step explanation:
2[tex]2\frac{5}{7} +4\frac{9}{14}[/tex]
15.99-15% discount +20%tip =
Answer:
$16.30
Step-by-step explanation:
15.99-15%=$13.59
13.59x1.20=$16.30
two numbers that multiply to -34 and add to -4
Answer: 4 an 34
Step-by-step explanation:
For which values of A, B,
and C
will Ax+By = C be a vertical line
through the point (9, 3)?
Answer:
See below
Step-by-step explanation:
A vertical line is just x =
so if a = 1 b = 0 and c = 9 would be a vertical line through the point
so you wind up with x = 9
Meldie made a cube whose side is (3x - 2) inches. Find its volume in cubic inches.
Answer:
x^2(3x-2) cubic inches OR in^3
OR
3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3
I AM UNAWARE IF YOU ASKED THAT ONE SIDE IS (3X-2) OR ALL. I WILL ANSWER BOTH PARTS
-
NOTE: '^' MEANS TO THE POWER OF..
-
Volume = v, abc = 3 sides of cube (height, width, length)
Using the formula for volume in a cube,
[tex]v = abc[/tex]
We can solve this.
If one side is (3x-2)in,
(3x-2)(x)(x) = v.... x are the other two sidesx^2(3x-2) = vx^2(3x-2) cubic inches OR in^3
If all sides are (3x-2)in,
Use the formula,
[tex](a - b) ^{3} = {a}^{3} + 3ab(b - a) - {b}^{3} [/tex]
We can solve this.
(3x-2)(3x-2)(3x-2) = v(3x-2)^3 = v.... 3x = a and -2 = b(3x)^3 + [(3)(3x)(2)][2-3x] - (2)^3 = v27x^3 + 18x(2-3x) -8 = v(27x^3 + 36x - 54x^2) - 8 = v.. Terms inside brackets - take 3x as common and leave out 83x(9x^2 -18x +12) = v... Take 3 as common again in the brackets3x [ 3 ([3x^2 -6x] + 4) -8 = v....Take 3x common in the terms in square brackets3x [ 3 [ 3x (x-2) + 4 ]] - 8 = v3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 = v3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3
___
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___
Round 57.183 to the nearest whole number tenth and hundredth
Answer:
Step-by-step explanation: 57.183= to the whole number= 58.183
Tenth= 57.180
Hundredth= 57.200
Answer:
Nearest Whole Number: 57
Nearest Tenth: 57.2
Nearest Hundredth: 57.18
*Note: When rounding to a place value the number after the place value you want determines whether the place value number says the same or goes up by 1. In order for the place value number to stay the same the number after has to be less than 5 and in order for the place value number to go up by 1 the number after has to be greater than or equal to 5.
