Answer:
$29.34.
Step-by-step explanation:
To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:
Current balance = previous balance + new charge
Current balance = $319 + $170
Current balance = $489
The minimum payment is 6% of the current balance:
Minimum payment = 6% x current balance
Minimum payment = 6% x $489
Minimum payment = $29.34
Therefore, the minimum payment on the credit card would be $29.34.
Answer:
$29.34.
Step-by-step explanation:
To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:
Current balance = $319 + $170 = $489
Minimum payment = 6% x $489 = $29.34
The minimum payment on the credit card would be $29.34.
Hope this helped, have a GOOD DAY!!!!!
What is the measure of side PQ?
Answer:
PQ is 35.6 units.
Step-by-step explanation:
From the problem, we can see that the smaller quatilateral is 4x smaller than the bigger one. We can multiply 8.9 by 4 to get 35.6 units.
Ann had a total of 285 red and blue beads. She used 45 red beads and 40% of the blue bead. After that,the ratio of the number of red beads to blue beads Ann had was 1:3.
Answer:
Let's start by figuring out how many blue beads Ann had initially.
If Ann had a total of 285 red and blue beads, and she used 45 red beads, then she had 240 blue beads remaining.
If Ann used 40% of the blue beads, then she used:
0.40 x 240 = 96 blue beads
After using 45 red beads and 96 blue beads, Ann had the following number of red and blue beads remaining:
Red beads = 285 - 45 = 240
Blue beads = 240 - 96 = 144
At this point, the ratio of red beads to blue beads is:
Red beads : Blue beads = 240 : 144 = 5 : 3
However, we want the ratio to be 1 : 3. To achieve this ratio, we need to divide both the red beads and blue beads by 5. This gives us:
Red beads = 240 / 5 = 48
Blue beads = 144 / 5 = 28.8
Since we can't have a fraction of a bead, we need to round up the number of blue beads to the nearest whole number. This gives us:
Red beads = 48
Blue beads = 29
Therefore, Ann initially had 285 - 48 - 29 = 208 beads, with 48 red beads and 29 blue beads.
Step-by-step explanation:
find the equation of the axis of symmetry of the parabola. each box in the grid represents $1$ unit.
According to the information, we can infer that the equation expressed by the parable symmetry axis is x = −b2a.
What is the axis of symmetry of a parable?The symmetry axis of a parable is a term that refers to a vertical line that divides the parable into two congruent halves. The axis of symmetry always passes through the vertex of the parable.
How to find the symmetry axis of this parable?To find the symmetry axis of this parable we must perform the following procedure taking into account the following information:
Graph the parabola y = x2−7x+2Additionally, we must compare the equation with y = ax2+bx+c to find the values of a, b, and c. Then these values would be like this:
A = 1B = −7C = 2According to the above, we can replace these values to solve the equation of axis of symmetry. then, the graph of a quadratic equation in the form Y = Ax2+Bx+C has ss its axis of symmetry the line X = −B2a.
Note: This Question is incomplete. Here is the complete information:
Attached Image
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a, b, c, and d are four different numbers and the proportion is true, which of the following is false?
If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, then none of the statements is false.
What is proportion?
In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
Since a/b = c/d, are proportional then can cross-multiply to get ad = bc.
Now, evaluate each statement -
A. b/a = d/c
Cross-multiplying, it is obtained that bc = ad, which is true based on the original proportion.
Therefore, this statement is true.
B. a/c = b/d
Cross-multiplying, it is obtained ad = bc, which is also true based on the original proportion.
Therefore, this statement is true.
C. b/a = c/d
This is equivalent to the original proportion, so it is true.
D. (a + b)/b = (c + d)/d
Simplify the equation -
d(a + b) = b(c + d)
da + db = bc + bd
da = bc
Cross-multiplying, it is obtained that da = bc, which is true based on the original proportion.
Therefore, this statement is true.
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FILL IN THE BLANK question 1 options: two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are ___and all corresponding sides are proportional.
Two polygons are similar if and only if all corresponding angles are congruent and all corresponding sides are proportional. The solution has been obtained by using concept of similar quadrilaterals.
What are similar quadrilaterals?
Two quadrilaterals are considered to be similar when two adjacent sides have the same ratio and all three matching angles are equal (the fourth angle automatically becomes equal because the internal angle sum equals 360 degrees).
Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.
Hence, the corresponding angles need to be congruent.
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6th grade math pls help
The ratio of people waiting in line for the slingshot is 2:21
What is ratioA ratio is a relationship between two quantities that expresses how many times one quantity is contained in the other. It can be expressed in different ways, such as with the use of a colon (:), a fraction (/), or the word "to.
From the question, the total number of people is 15 + 4 + 12 + 11 = 42
The number of people waiting for slingshot is = 4
The ratio of slingshot waiting in line = 4/42
The ratio = 2:21
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Factorise 2 + x^3 - 3x^6
answer is (2 + 3x^3)(1 - x)(1 + x + x^2)
need working out
Let w = x^3
Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6
In short: w^2 = x^6
The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2
Set this equal to zero and use the quadratic formula. We'll plug in
a = -3b = 1c = 2So,
[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\[/tex]
If w = -2/3, then that rearranges to the following
w = -2/3
3w = -2
3w+2 = 0
This makes (3w+2) a factor of -3w^2+w+2
If w = 1, then it rearranges to w-1 = 0.
This makes (w-1) a factor of -3w^2+w+2
--------------------
To summarize the previous section, we found the factors of -3w^2+w+2 were:
(3w+2)(w-1)It leads to (3w+2)(w-1)
We must stick a negative out front because the leading coefficient is negative.
Therefore, -3w^2+w+2 = -(3w+2)(w-1)
You can use the FOIL rule to confirm.
--------------------
Recall we made w = x^3
Let's replace each w with x^3
-(3w+2)(w-1)
-(3x^3+2)(x^3-1)
This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)
The next task is to factor x^3-1 using the difference of cubes factoring rule.
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)
x^3 - 1 = (x-1)(x^2 + x + 1)
--------------------
So,
2+x^3-3x^6
-3x^6 + x^3 + 2
-(3x^3+2)(x^3-1)
-(3x^3+2)(x-1)(x^2 + x + 1)
-(2 + 3x^3)(-(1-x))(1 + x + x^2)
(2 + 3x^3)(1 - x)(1 + x + x^2)
Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.
Find the value of
X
Z
Y
Answer:
x = 40° , y = 43° , z = 97°
Step-by-step explanation:
∠ DAC = y = ∠ ACB = 43°
• opposite angles in a parallelogram are congruent , then
z = ∠ D = 97°
the sum of the 3 angles in Δ ACD = 180° , that is
x + y + 97° = 180°
x + 43° + 97° = 180°
x + 140° = 180° ( subtract 140° from both sides )
x = 40°
then
x = 40° , y = 43° , z = 97°
government data show that 8% of adults are full time college students and that 21% of adults are age 65 or older. if an adult is randomly selected, is p(full time college student and 65 or older)
We do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.
What is Probability ?Probability is a method for assessing how likely something is to happen. Many occurrences cannot be foreseen with 100% accuracy. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
We cannot determine whether the probability of an adult being a full-time college student and 65 or older is nonzero based on the given information alone.
To see why, consider the following two scenarios:
Scenario 1: The proportion of adults who are both full-time college students and 65 or older is 0%.
In this case, the events "full-time college student" and "65 or older" are mutually exclusive. That is, no adult can be both a full-time college student and 65 or older. Therefore, P(full-time college student and 65 or older) = 0%.
Scenario 2: The proportion of adults who are both full-time college students and 65 or older is greater than 0%.
In this case, the events "full-time college student" and "65 or older" are not mutually exclusive. That is, there may be some adults who are both full-time college students and 65 or older. Therefore, P(full-time college student and 65 or older) is greater than 0%.
Since we do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.
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If a plank has a perimeter of 18 feet and an area of 14 square feet what mostly describes the length and the width of the plank
Answer:
length =7 breadth =2
Step-by-step explanation:
l x b = 14, so l= 14/b
2(l+b) =18 , l+b =9
14/b+b=9
[tex]b^ {2}[/tex] -9b+14=0
[tex]b^ {2}[/tex] -7b-2b+14=0
(b-7)(b-2) =0
b= 7 or 2
A triangular prism has height 8 units. The base of the prism is shown in the image. What is the volume of the prism? Round your answer to the nearest tenth.
Do not include units (cubic units) in your answer.
The volume of the triangular prism is 137.2 units cube.
How to find the volume of a triangular prism?The triangular prism has a height of 8 units. The base of the prism is shown in the image. The volume of the prism can be represented as follows:
volume of a triangular prism = BH
where
B = base areaH = heightTherefore, let's find the base area
B = 1 / 2 b h
let's find b
Hence,
tan 65 = b / 4
cross multiply
b = 4 tan 65
b = 8.57802768204
b = 8.58 units
Therefore,
B = 1 / 2 × 4 × 8.58
B = 17.1560553641
Therefore,
volume of a triangular prism = 17.156 × 8
volume of a triangular prism = 137.248442913
Hence,
volume of a triangular prism = 137.2 units cube
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Plot the following points in the Cartesian plane.
{(3,6),(−8,2),(−9,−4),(2,−8)}
What is cartesian plane ?
A Cartesian plane (also known as a coordinate plane or rectangular coordinate system) is a two-dimensional plane formed by two perpendicular number lines, referred to as the x-axis and the y-axis, that intersect at a point called the origin. The x-axis is a horizontal line, and the y-axis is a vertical line.
Explanation:
To plot the following points in the Cartesian plane:
{(3,6),(-8,2),(-9,-4),(2,-8)}
First, we draw the x and y axes to form a Cartesian plane.
Then, for each point, we plot the x and y coordinates on the graph. The x coordinate indicates the horizontal position of the point on the x-axis, while the y coordinate indicates the vertical position of the point on the y-axis.
The point (3,6) is plotted as a dot on the Cartesian plane located 3 units to the right of the origin on the x-axis and 6 units above the origin on the y-axis.
The point (-8,2) is plotted as a dot located 8 units to the left of the origin on the x-axis and 2 units above the origin on the y-axis.
The point (-9,-4) is plotted as a dot located 9 units to the left of the origin on the x-axis and 4 units below the origin on the y-axis.
The point (2,-8) is plotted as a dot located 2 units to the right of the origin on the x-axis and 8 units below the origin on the y-axis.
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Sunny earns
$
12
$12dollar sign, 12 per hour delivering cakes. She worked for
�
xx hours this week. Unfortunately, she was charged
$
15
$15dollar sign, 15 for a late delivery on Tuesday.
How much money did Sunny earn this week?
Therefore , the solution of the given problem of expression comes out to be Sunny earned $12x - 15 this week.
Expression : What is it?Mathematical operations like addition, multiply, and division are necessary. They result in the following when combined: An equation, some information, and a mathematical operator Values, parameters, and arithmetic calculations like additions, subtractions, multiplication and division, and divisions are all found in a statement of fact. Different sentences and words can be contrasted and compared.
Here,
If Sunny worked for x hours and earns $12 per hour, her earnings before the late delivery charge would be:
$12x$
However, since she was charged $15 for the late delivery on Tuesday, her earnings for the week would be:
$12x - 15$
Therefore, Sunny earned $12x - 15 this week.
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The complete question is "Sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did Sunny earn this week?"
Find domain Range Y-intercept X- intercept Vertical asymptote Horizontal asymptote Pic attached below note write domain and range in interval notation
Find domain
Range
Y-intercept
Xi intercept
Vertical asymptote
Horizontal asymptote
Pic attached below
The key features of this rational function include the following:
Domain: (-∞, 2) ∪ (2, ∞)
Range: (-∞, -2) ∪ (-2, ∞)
Y-intercept: -7/2.
X-intercept: 7/2.
Vertical asymptote: x = 2.
Horizontal asymptote: y = -2.
What is a rational function?In Mathematics, a rational function simply refers to a type of function which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:
NumeratorDenominatorAdditionally, the horizontal extent of any graph of a rational function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.
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X/-3 is greater or equal to 23
The solution to the inequality is any value of X that is less than or equal to -69.
What is Inequality?
An inequality is a relationship that compares two numbers or other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.
The inequality X/(-3) ≥ 23 can be solved as follows:
We begin by multiplying both sides of the inequality by -3, which will reverse the direction of the inequality since we are multiplying by a negative number. This gives:
X ≤ -69
Therefore, the solution to the inequality is any value of X that is less than or equal to -69.
In interval notation, we can write the solution as:
(-∞, -69]
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The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Read the following sentence.
The grizzly bear ambled across the meadow, uprooting logs in search of the delicious grubs that tunneled beneath
Which words belong in the blank?
O her
O it
O him
them
Answer: it
Step-by-step explanation:
. Corey has a piece of teak wood that is three times as long as his piece of oak wood. He
says that he can use two different equations to find out how long his piece of teak wood is
compared to his piece of oak wood. Is he correct? Explain your reasoning.
Corey's piece of oak wood is 8 inches long. Write and solve an equation to find the length of
mis teak wood piece.
The equation and solution to find the length of mis teak wood piece is x=3*8 and 24.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The length of oak wood=8inches
Teak wood= 3* oak wood
Now,
Let the length of teak wood be x
Then,
x=3*8
x=24
Therefore, by algebra the answer will be 24.
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HELP ASAP!I WILL GIVE YOU BRAINLIST IF YOU ANSWER!
The areas and the perimeters of the composite figures are listed below:
Case 1: A = 36 cm² (Right choice: A)
Case 2: p = 30 cm (Right choice: G)
Case 3: A = 46 cm² (Right choice: I)
Case 4: p = 38 cm (Right choice: H)
How to determine the perimeter and the area of a composite figure
In this problem we find two composite figures that are result of combining three rectangles, whose perimeters are the sum of all side lengths and whose areas are the sum of the areas of the rectangles. The formulae for the perimeter and the area of a rectangle are, respectively:
Perimeter
p = 2 · (w + l)
Where:
p - Perimeter, in centimeters.w - Width, in centimeters.l - Height, in centimeters.Area
A = w · l
Where A is the area, in square centimeters.
Now we proceed to determine the perimeters and areas according to the case:
Case 1
A = 2 · (3 cm) · (5 cm) + (2 cm) · (3 cm)
A = 30 cm² + 6 cm²
A = 36 cm² (Right choice: A)
Case 2
p = 2 · (3 cm) + 3 · (2 cm) + 2 · (5 cm) + 8 cm
p = 6 cm + 6 cm + 10 cm + 8 cm
p = 30 cm (Right choice: G)
Case 3
A = 2 · (5 cm) · (4 cm) + (2 cm) · (3 cm)
A = 40 cm² + 6 cm²
A = 46 cm² (Right choice: I)
Case 4
p = 2 · (4 cm) + 2 · (5 cm) + 2 · (2 cm) + 3 cm + 13 cm
p = 8 cm + 10 cm + 4 cm + 3 cm + 13 cm
p = 38 cm (Right choice: H)
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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Answer:
Step-by-step explanation:
4x-22.2=1.90
22.20-4x=1.90
4x + 1.90 = 22.20
if 2 apples can be bought in Rs 48 , how many apples can be bought in Rs 1098 ?
don't spam-
tysm! :)
Answer:
Rs 1098 can buy 45.75 apples (or approximately 45 apples, since we cannot buy a fractional part of an apple).
Step-by-step explanation:
We can use proportionality to solve this problem. Since the price of apples is directly proportional to the number of apples, we can set up a proportion:
2 apples / Rs 48 = x apples / Rs 1098
To solve for x, we can cross-multiply and simplify:
2 * Rs 1098 = 48 * x
Rs 2196 = 48x
x = Rs 2196 / 48
x = 45.75
Therefore, Rs 1098 can buy 45.75 apples (or approximately 45 apples, since we cannot buy a fractional part of an apple).
Determine if each sets of numbers can be the lengths of the sides of a right triangle. YES or NO for each please.
The result of each length of the sides of a right triangle is as follows:
5, 12 and 13: Yes
12, 35 and 20√5: No
5, 10 and 5√5: Yes
8, 12 and 15: No
20, 99 and 101: Yes
How to determine if each sets of numbers can be the lengths of the sides of a right triangle?Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.
For 5, 12 and 13:
13² = 5² + 13²
169 = 169 (This is true)
YES
For 12, 35 and 20√5 :
(20√5)² = 12² + 35²
2000 = 1369 (This is false)
NO
For 5, 10 and 5√5 :
(5√5)² = 5² + 10²
125 = 125 (This is true)
YES
For 8, 12 and 15:
15² = 12² + 15²
225 = 369 (This is false)
NO
For 20, 99 and 101:
101² = 20² + 99²
10201 = 10201 (This is true)
YES
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Which point on the number line best represents –1?
Answer:
R
Step-by-step explanation:
-1 is exactly between 0 and -2, meaning that the answer is R.
R is the right answer
: The circulation (as of September 20 of each year) of daily English-language newspapers in a certain country between 1986 and 2000 can be modeled as n(x) = 0.00692x^3 - 0.42x^2 + 3.557x + 51.588 million newspapers where x is the number of years since 1980. What was the average newspaper circulation from 1986 through 2000. (Round your answer to three decimal places.) In what year was the newspaper circulation closest to the average circulation from 1986 through 2000? (Round your answer up to the nearest integer.)
The average from 1986 to 2000 was 46.250 million and circulation was closest to 46.250 in 1994.
What is the definition of average?
An average of a list of data is a mathematical expression for the centre value of a set of data. It is defined mathematically as the ratio of the sum of all the data to the number of units in the list. The average of 2, 3, and 4 equals (2+3+4)/3 = 9/3 = 3.
Average = Sum of Values divided by Number of Values
Now,
As The newspaper circulation between 1986 and 2000 can be modeled as:
n(x)=0.00692x³-0.42x²+3.557x+51.588 million newspaper, where x is the number of years since 1980.
1. We will determine the circulation by finding x (subtracting 1980 from the said year) and substitute it in the formula.
n(6)=59.305, n(7)=59.281, n(8)=58.707, n(9)=57.626, n(10)=56.078, n(11)=54.106, n(12)=51.750, n(13)=49.052, n(14)=46.054, n(15)=42.798, n(16)=39.324, n(17)=35.675, n(18)=31.891, n(19)=28.015, n(20)=24.088
2. We will add the values: Sum of n=693.750
3. Average newspaper circulation=Sum of circulation each year/No of years
Average=693.750/15=46.250
4. Compare each year circulation to the average.
The circulation in 1994 i.e.,46.054 was closest to the average i.e.,46.250
As a result, the average newspaper circulation from 1986 to 2000 was 46.25 million. Additionally, the year with the closest average circulation from 1986 to 2000 was 1994.
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given pseudo code, write the method in JAVA, pseudocode had different parameters PLEASE WRITE WITH ONLY INT[] ARR AS PARAMETER
public static Triple getMaxSubArray(int[] arr) This method returns a triple that represents the maximum subarray. The first element of the triple is the index in arr where the maximum subarray starts, the middle element of the triple is where the index in the arr where maximum subarray ends, and the last element of the triple is the maximum subarray sum
findMaxSubarry(arr,low,high)
if high==low return (low,high,arr[low])
else
mid = mid point of arr
(l-low,l-high,l-sum) = findMaxSubarray(arr,low,mid)
(r-low,r-high,r-sum) = findMaxSubarray(arr,mid+1,high)
c-low,c-high,c-sum) = findMaxCrossing(arr,low,mid,high)
if l-sum ≥ r-sum and l-sum ≥ c-sum
return (l-low,l-high,l-sum)
else if r-sum ≥l-sum and r-sum ≥ c-sum
return (r-low,r-high,r-sum)
else
return (c-low,c-high,c-sum)
findMaxCrossing(arr,low,mid,high)
l-sum = MIN
sum = 0
for i=mid downto low
sum = sum arr[i]
if sum > l-sum
l-sum = sum
max-left = i
r-sum = MIN
sum = 0
for j=mid+1 to high
sum = sum + arr[j]
if sum > r-sum
r-sum = sum
max-right = j
return (max-left,max-right,l-sum+r-sum);
The Pseudocode is discussed below.
What is JAVA?Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible.
Given is to write a Pseudo code.
In computer science, pseudo - code is a plain language description of the steps in an algorithm or another system.Pseudo - code often uses structural conventions of a normal programming language, but is intended for human reading rather than machine reading.Pseudocode is an artificial and informal language that helps programmers develop algorithms. Pseudocode is a "text-based" detail (algorithmic) design tool is an artificial and informal language that helps programmers develop algorithms. Pseudocode is a "text-based" detail (algorithmic) design toolTherefore, the Pseudocode is discussed above.
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Calculus, I need help for these exercises
Value of limit expression
[tex]\lim_{\theta \to 0} \dfrac{10\theta}{3sin\theta}[/tex] [tex]=\dfrac{5}{9}[/tex]
Value of limit expression
[tex]\lim_{x \to 1} \dfrac{sin(x -1)}{x^{2} + 5x - 6}[/tex] [tex]= \dfrac{1}{7}[/tex]
What is limit?In mathematics, the limit is the value that the function approaches as the input approaches the value. Limits are essential in calculus and mathematical analysis and are used to define continuity, derivatives and integrals
Given
[tex]a) \lim_{\theta \to 0} \dfrac{10\theta}{3sin\theta}[/tex]
[tex]\dfrac{10}{3} \lim_{\theta \to 0} \dfrac{\theta}{sin6\theta}[/tex]
[tex]sin\theta = \theta - \dfrac{\theta^{3}}{3!} + \dfrac{\theta^{5}}{5!} + .......[/tex]
[tex]\dfrac{10}{3} \lim_{\theta \to 0} \dfrac{\theta}{6\theta - \dfrac{(6\theta)^{3} }{3!} +\dfrac{(6\theta)^{5} }{5!}- ......}[/tex]
[tex]\dfrac{10}{3} \lim_{\theta \to 0} \dfrac{\theta}{(6\theta)(1 - \dfrac{(6\theta)^{2} }{3!} +\dfrac{(6\theta)^{4} }{5!}- ......)}[/tex][tex]\dfrac{10}{3\times6} \lim_{\theta \to 0} \dfrac{\theta}{(\theta)(1 - \dfrac{(6\theta)^{2} }{3!} +\dfrac{(6\theta)^{4} }{5!}- ......)}[/tex][tex]\dfrac{10}{3\times6} \lim_{\theta \to 0} \dfrac{1}{(1 - \dfrac{(6\theta)^{2} }{3!} +\dfrac{(6\theta)^{4} }{5!}- ......)}[/tex]
[tex]\dfrac{10}{3\times6} \times \dfrac{1}{(1 - \dfrac{(0)^{2} }{3!} +\dfrac{(0)^{4} }{5!}- ......)}[/tex]
[tex]=\dfrac{5}{9}[/tex]
[tex]b)\lim_{x \to 1} \dfrac{sin(x -1)}{x^{2} + 5x - 6}[/tex]
[tex]\lim_{x \to 1} \dfrac{(x -1) - \dfrac{(x - 1)^{3}}{3!}-\dfrac{(x - 1)^{5}}{5!} - ......}{x^{2} + 6x - x -6}[/tex][tex]\lim_{x \to 1} \dfrac{(x -1) - \dfrac{(x - 1)^{3}}{3!}-\dfrac{(x - 1)^{5}}{5!} - ......}{x(x + 6) - 1(x +6)}[/tex][tex]\lim_{x \to 1} \dfrac{(x - 1)(1 - \dfrac{(x - 1)^{2}}{3!}-\dfrac{(x - 1)^{4}}{5!} - ......)}{(x- 1)(x +6)}[/tex]
[tex]\dfrac{(1 - \dfrac{(1 - 1)^{2}}{3!}-\dfrac{(1 - 1)^{4}}{5!} - ......)}{(1 +6)}[/tex]
[tex]=\dfrac{1}{7}[/tex]
Hence, [tex]\dfrac{5}{9}[/tex] is value of limit expression [tex]\lim_{\theta \to 0} \dfrac{10\theta}{3sin\theta}[/tex]
and [tex]\dfrac{1}{7}[/tex] is value of expression [tex]\lim_{x \to 1} \dfrac{sin(x -1)}{x^{2} + 5x - 6}[/tex]
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
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Answer:
x=-15, y=26
Step-by-step explanation:
A student concludes that the solution to the equation x+3=2x-4, in one variable, is the x-coordinate of the solution to the graph of this linear system.
x-y=-3
2x-y=4
Which statement justifies this conclusion based on the student's work?
A Each side of the equation, in one variable, can be found by isolating the x-variable of each equation
in the system. The solution is the y-coordinate, where the x-coordinates of both graphs are the
same.
B Each side of the equation, in one variable, can be found by isolating the y-variable of each equation
in the system. The solution is the x-coordinate, where the x- coordinates of both graphs are the
same.
C. A solution to both equations in the system is (7, 10). Since that point is where the equations
intersect, it must be the solution to the system.
D. The solution to the equation, in one variable, is x = 7. Since both equations in the system have
y-values when x = 7, it must be the solution to the system.
Answer:based on the student's work?A Each side of the equation, in one variable, can be found by isolating the x-variable of each equationin the s
Step-by-step explanation:
Chart that arranges all of the known elements in a particular order.
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
Rearrange unknown terms to the left side of the equation: [tex]x-2x = -4 - 3[/tex]
Combine like terms: [tex]-x = -4-3[/tex]
Calculate the sum or difference: [tex]-x = -7[/tex]
Divide both sides of the equation by the coefficient of variable: [tex]x = 7[/tex]
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A. The height of the cuboid is 2.5 cm.
B. The suggested dimensions of the cuboid is 25 x 5 x 1.
What is the volume of a figure?The volume of a given three dimensional figure is the total quantity of matter that it can contained. Thus various figures has different methods of determining their volume.
volume of a cube = length x length x length
= (length)^3
volume of a cuboid = length x width x height
Considering the given question, since the volumes of the cube and cuboid are the same, then we have:
volume of a cube = volume of a cuboid
(length)^3 = length x width x height
5^3 = 10 x 5 x height
125 = 50 x height
height = 125/ 50
= 2.5
The height of the cuboid is 2.5 cm.
B. volume of the cuboid = length x width x height
= 10 x 5 x 2.5
= 125 cm^3
Thus possible dimensions for the cuboid 25 x 5 x 1.
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A survey was conducted that asked 1002 people how many books they had read in the past year. Results indicated that x overbar equals 11. 3 books and sequals16. 6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval
The 90% confidence interval for the mean number of books people read is (-16, 38.6).
How to construct a 90% confidence interval for the mean number of books people read?To construct a 90% confidence interval for the mean number of books people read, we first need to find the critical value (z*) that corresponds to a 90% confidence level. This can be found using a z-table or calculator. The critical value for a 90% confidence level is 1.645.
Next, we need to calculate the margin of error (ME) using the formula ME = z* x SE, where SE is the standard error. In this case, SE = 16.6 books, so ME = 1.645 x 16.6 = 27.3 books.
Finally, we can construct the 90% confidence interval by adding and subtracting the margin of error from the sample mean (x overbar). The confidence interval is:
(x overbar - ME, x overbar + ME) = (11.3 - 27.3, 11.3 + 27.3) = (-16, 38.6)
This means that we are 90% confident that the true mean number of books people read is between -16 and 38.6 books.
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