Answer:
Step-by-step explanation:
Yesterday, Lily withdrew $25 from her savings account to buy a birthday gift for her grandfather.
What integer represents the change in Lily's account balance?
The integer number that represents the change in Lily's account balance is given as follows:
-25.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
For the balance of the bank account, we have that:
Deposits are represented by positive integers.Withdraws are represented by negative integers.Lily withdrew $25 from her savings account to buy a birthday gift for her grandfather, hence the integer number is given as follows:
-25.
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Which of the following options represents the phrase "eight less than the quotient of 24 and 12"?
Hello!:
24/12 - 8
= 2 - 8
= -6
Here, S.P. = . 1,61, 680 D%= 6%. M.P. = ?
The marked price (M.P.) is 1,72,000 when the selling price is 1,61,680 with discount of 6%.
To find the marked price (M.P.), we can use the formula:
M.P. = S.P. / (1 - D%)
Given:
S.P. = 1,61,680
D% = 6%
First, we need to convert the discount percentage to decimal form by dividing it by 100:
D% = 6/100 = 0.06
Now, we can substitute the values into the formula:
M.P. = 1,61,680 / (1 - 0.06)
M.P. = 1,61,680 / 0.94
M.P. = 1,72,000
Therefore, the marked price (M.P.) is approximately 1,72,000.
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Select the correct answer. Which value of x from the set [4, 5, 6, 7), makes this equation true? 4(8-x) = 8 OB. 5 OC. OD. 7 C. 6
Answer:
6
Step-by-step explanation:
The correct answer is C. 6.
If we substitute 6 for x in the equation, we get 4(8-6) = 4(2) = 8.
This is the only value of x that makes the equation true.
Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
6543/2
-24
1-3-
J
ہے
Answer:
(a) x-intercept = -2
(b) y-intercept = 4
ہے
8. A randomized controlled trial was designed to compare the effectiveness of splinting versus
surgery in the treatment of carpal tunnel syndrome. Results are given in the table. The results
are based on evaluations made one year after the treatment. Using a 0.01 significance level,
find the test statistic and critical value needed to test the claim that the success is independent
of the type of treatment.
Splint treatment
Surgery treatment
Successful
Treatment
60
67
Otest statistic = 0.848, critical value = 6.635
statistic 9 750 critical value = 6.635
Unsuccessful
Treatment
23
6
(1 poir
The test statistic and critical value needed to test the claim that the success is independent of the type of treatment are 9.750 and critical value is 6.635.
How to calculate the valueThe expected value for each cell is calculated as follows:
E = row total * column total / grand total
The grand total is 150.
The row totals are 83 and 67.
The column totals are 86 and 64.
The expected values are as follows:
Successful: 60 * 86 / 150 = 36.4
Unsuccessful: 60 * 64 / 150 = 29.6
Surgery treatment
Successful: 67 * 86 / 150 = 49.6
Unsuccessful: 67 * 64 / 150 = 27.4
The test statistic is calculated as 9.750
The critical value is calculated as follows:
α = 0.01
df = (r-1)(c-1) = (2-1)(2-1) = 1
x²(α, df) = 6.635
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A circle is inscribed inside a square of a side length of 10 cm. What is the area inside the square and outside the circle
Answer:
The figure is omitted--please sketch it to confirm my answer.
[tex]\pi {(5 \sqrt{2}) }^{2} - {10}^{2} [/tex]
[tex]50\pi - 100 = 50(\pi - 2) = 57.08[/tex]
The area inside the square and outside the circle is about 57.08 cm^2.
The manufacturer of a DVD player has found the revenue R (in dollars) is R(p) = -4p² + 1700p,
when the unit price is p dollars. What is the maximum revenue to the nearest whole dollar?
a. $722,500
c. $180,625
b. $1,445,000
d. $361,250
The maximum revenue, to the nearest whole dollar, is $180,625 (option c).
To find the maximum revenue, we need to determine the vertex of the quadratic function represented by the revenue equation.
The revenue equation is given as:
R(p) = -4p² + 1700p
The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula:
x = -b / (2a)
For the given revenue equation, a = -4 and b = 1700. Plugging these values into the formula, we have:
p = -1700 / (2 × -4)
p = -1700 / -8
p = 212.5
The maximum revenue occurs at p = 212.5.
To find the maximum revenue, we substitute this value back into the revenue equation:
R(p) = -4(212.5)² + 1700(212.5)
R(p) = -4(45256.25) + 361250
R(p) = -181025 + 361250
R(p) = 180625
Therefore, the maximum revenue, to the nearest whole dollar, is $180,625 (option c).
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which of the following is the slope of the line with equation -7x=6+3y
Answer:
Slope = -7/3
Step-by-step explanation:
-7x = 6 + 3y is in the standard form of a line, whose general equation is
Ax = C + By (it's sometimes written in terms of C and is Ax + By = C, but in this problem, it's written in terms of Ax).
We can find the slope of the line by converting from standard form to slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-intercept.Step 1: Subtract 6 from both sides:
(-7x = 6 + 3y) - 6
-7x - 6 = 3y
Step 2: Divide both sides by 3 to isolate y:
(-7x - 6 = 3y) / 3
-7/3x - 2 = y
Thus, the slope of the line is -7/3
Answer: Therefore the slope is [tex]-\frac{7}{3}[/tex].
Step-by-step explanation:
We can rewrite the equation -7x=6+3y in slope-intercept form y = mx + b, where the m is the slope of the line, and b is the y-intercept.
-7x = 6 + 3y
-6 -6
-7x - 6 = 3y
[tex]\frac{-7x}{3}-\frac{6}{3} =\frac{3y}{3}[/tex]
[tex]\frac{-7}{3}x-2 =y[/tex]
Therefore the slope is [tex]-\frac{7}{3}[/tex].
Enter the number that belongs in the green box
The number in the green box is 31.78° .
Given,
Triangle with sides 11 , 12 , 20.
From Cosine Law.
Let △ABC have sides a, b, c.
Here,
a = 11
b = 20
c = 12
Length of the side opposite vertex A is called a.
Length of the side opposite vertex B is called c.
Length of the side opposite vertex C is called c.
Let θ = ∠C
Then, the Cosine Law says that
c²=a²+b²−2abcosθ.
Substitute the values of a , b , c .
12² = 11² + 20² - 2 × 11× 20 cosθ
θ = 31.78°
Hence the angle can be found out from cosine law.
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Jonah's swimming pool is 21 meters by 20 meters. He swam from one corner of the pool to the opposite corner. How far did Jonah swim?
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
To determine how far Jonah swam from one corner of the pool to the opposite corner, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
[tex]Hypotenuse^2 = Length^2 + Width^2[/tex]
[tex]Hypotenuse^2[/tex] =[tex]21^2 + 20^2[/tex]
[tex]Hypotenuse^2[/tex]= 441 + 400
[tex]Hypotenuse^2[/tex]= 841
Taking the square root of both sides, we find:
Hypotenuse =[tex]\sqrt{841[/tex]
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
The two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
[tex]Hypotenuse^2 = Length^2 + Width^2\\Hypotenuse^2 = 21^2 + 20^2\\Hypotenuse^2 = 441 + 400\\Hypotenuse^2 = 841[/tex]
Taking the square root of both sides, we find:
Hypotenuse = [tex]\sqrt841[/tex]
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
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100 Points! Geometry question. Photo attached. Find the measure. Please show as much work as possible. Thank you!
Answer:
The answer would lie within 31 degrees of MP and also as in PM.
Answer:
central m arc MP=118°
Step-by-step explanation:
here
central m arc MN=2* inscribed m arc MN=2*31=62°
again
central m arc MN+ central m arc MP=180° being linear pair
substituting value
62°+central m arc MP=180°
central m arc MP=180°-62°
central m arc MP=118°
Please help i will give brainliest
The value of measure of angle 1, angle 2, and angle 3 are,
⇒ ∠1 = 106 degree
⇒ ∠2 = 74°
⇒ ∠3 = 74°
We have to given that;
Angle in figure is,
⇒ 74°
Since, From figure,
angle 1 is,
⇒ ∠1 = 180 - 74
⇒ ∠1 = 106 degree
Hence, We get;
Measure of angle 2 is,
⇒ ∠2 = 180 - 106
⇒ ∠2 = 74°
And, Measure of angle 3 is,
⇒ ∠ 3 = ∠ 2
By definition of alternate interior angle.
⇒ ∠3 = 74°
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The measure of ∠1 is 106 because it is a straight angle with 74° angles.
The measure of ∠2 is 74 because it is a vertical angle with 74° angles.
The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.
We have,
The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
Now,
∠1 + 74 = 180
∠1 = 180 - 74
∠1 = 106
And,
∠2 and 74 are vertical angles.
So,
∠2 = 74
And,
∠3 and 74 are corresponding angles.
So,
∠3 = 74
Thus,
The measure of ∠1 is 106 because it is a straight angle with 74° angles.
The measure of ∠2 is 74 because it is a vertical angle with 74° angles.
The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.
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Simplify the following expression.
(6m5g5) 2
The simplified exponential expression in the context of this problem is given as follows:
[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]
How to simplify the exponential expression?The exponential expression in the context of the problem is defined as follows:
[tex](6m^5g^5)^2[/tex]
The power of a power rule is used when a single base is elevated to multiple exponents, and states that simplified expression is obtained keeping the base, while the exponents are multiplied.
Applying the exponent of 2, we have that:
6² = 36.5 x 2 = 10.Hence the simplified exponential expression in the context of this problem is given as follows:
[tex](6m^5g^5)^2 = 32m^{10}g^{10}[/tex]
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Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Volume = $\ 10,000\pi\ $ in.3
A cylindrical piece of a log is shown. The diameter of its base is 32 inches and height is h.
$h\ \approx$
in.
The nearest Whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
The missing dimension of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Given that the volume is 10,000π in³ and the diameter of the base is 32 inches, we can determine the radius (r) of the cylinder.
The diameter is twice the radius, so the radius is half of the diameter:
r = 32 inches / 2 = 16 inches
Substituting the known values into the volume formula, we have:
10,000π in³ = π * (16 in)^2 * h
Cancelling out the common factor of π, we get:
10,000 = 16^2 * h
Simplifying further:
10,000 = 256 * h
To isolate h, we divide both sides of the equation by 256:
h = 10,000 / 256
Calculating the value of h:
h ≈ 39.06
Rounded to the nearest whole number, the missing dimension (height) of the cylinder is approximately 39 inches.
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If s(x) = 2x² and f(x) = 3x, which value is equivalent to (s-f)(-7)?
O-439
O-141
O 153
O 443
The value of expression (s - f) (- 7) would be,
⇒ (s - f) (- 7) = 119
We have to given that,
Functions are defined as,
⇒ s (x) = 2x²
⇒ f (x) = 3x
Now, We can find the value of (s - f) (- 7) is,
⇒ (s - f) (- 7)
⇒ s (- 7) - f (- 7)
⇒ 2 (- 7)² - (3 × - 7)
⇒ 2×49 + 21
⇒ 98 + 21
⇒ 119
Therefore, The value of expression (s - f) (- 7) would be,
⇒ (s - f) (- 7) = 119
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PLEASE HELP AS SOON AS POSSIBLE !
The diameter, , of a sphere is 14.6. Calculate the sphere's volume, .
Use the value 3.14 for pi , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The volume of the sphere, given that the sphere has a diameter of 14.6 mm is 1628.7 mm³
How do i determine the volume of the sphere?The following data were obtained from the question:
Diameter (D) = 14.6 mmRadius (r) = Diameter (D) / 2 = 14.6 / 2 = 7.3 mmPi (π) = 3.14Volume of sphere =?The volume of a sphere is giving by the following formula
Volume of sphere = 4/3πr³
Inputting the given parameters, we can obtain the volume of the sphere as follow:
Volume of sphere = (4/3) × 3.14 × 7.3³
Volume of sphere = (4/3) × 3.14 × 389.017
Volume of sphere = 1628.7 mm³
Thus, we can conclude from the above calculation that the volume of the sphere is 1628.7 mm³
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What is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
The area of the rhombus is 100 mm². The Option D.
What is the area of the rhombus?To get area of a rhombus, we will use the formula: Area = (d₁ * d₂) / 2 where d₁ and d₂ are the lengths of the diagonals.
Given that the horizontal diagonal length is 25 millimeters (d₁ = 25 mm) and the vertical diagonal length is 8 millimeters (d₂ = 8 mm.
We will substitute values into the formula:
Area = (25 mm * 8 mm) / 2
Area = 200 mm² / 2
Area = 100 mm².
Full question:
A rhombus with horizontal diagonal length 25 millimeters and vertical diagonal length 8 millimeters. what is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
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Descrive in words the rule that is used to determine the term value from its position in the sequence
The rule used to determine the term value from its position in the sequence is often referred to as the "nth term" rule.
What is the nth-term rule?The nth-term rule involves identifying a pattern or relationship between the position (n) of a term in the sequence and the value of that term.
By analyzing the pattern, such as the common difference or common ratio, the nth-term rule allows us to express the value of any term in the sequence based on its position.
This rule provides a formula or equation that relates the position of a term to its corresponding value in the sequence.
Mathematically, the rule is:
T(n) = a + (n - 1) * d
where:
T(n) represents the value of the term at position n.a represents the first term in the sequence.n represents the position or index of the term in the sequence.d represents the common difference (for arithmetic sequences) or the common ratio (for geometric sequences) between consecutive terms.More on sequence and series can be found here: https://brainly.com/question/15583579
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Triangle ABC, with vertices A(-9,-8), B(-2,-9), and C(-8,-5), is drawn inside a rectangle. What is the area, in square units, of triangle ABC?
The area of triangle ABC is 19 square units.
To find the area of a triangle, we can use different formulas depending on the information available. Since we have the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can use the Shoelace Formula (also known as the Gauss's area formula) to calculate the area of the triangle.
The Shoelace Formula states that if the coordinates of the vertices of a triangle are (x1, y1), (x2, y2), and (x3, y3), then the area (A) of the triangle can be calculated as:
Area = 0.5 * |(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))|
Using the coordinates of the vertices A(-9, -8), B(-2, -9), and C(-8, -5), we can substitute these values into the formula to calculate the area.
Let's calculate step by step:
x1 = -9
y1 = -8
x2 = -2
y2 = -9
x3 = -8
y3 = -5
Area = 0.5 * |(-9 * (-9 - (-5)) + (-2) * (-5 - (-8)) + (-8) * ((-8) - (-9)))|
Area = 0.5 * |(-9 * (-4) + (-2) * (3) + (-8) * (-1))|
Area = 0.5 * |(36 + (-6) + 8)|
Area = 0.5 * |(38)|
Area = 0.5 * 38
Area = 19
Therefore, the area of triangle ABC is 19 square units.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
B. 108 ft³
Step-by-step explanation:
solution given:
We have Volume of solid = Area of base * length
over here
base : 9ft
height : 6 ft
length : 4ft
Now
Area of base : Area of traingle:½*base*height=½*9*6=27 ft²
Now
Volume : Area of base*length
Volume: 27ft²*4ft
Therefore Volume of the solid=108 ft³
Saleema
was investigating the newspaper subscriptions
for her local newspaper. At the beginning of the year,
She noted 1000 subscriptions for
Subscribed to the newspaper. The number of subscriptions
left y years,
a small area that
left
Y years after 2012 is represented by the function
shown.
N (y) = 1000 (0.5)Y
Part A
Approximately how many subscriptions were left when
y=5?
Based on the information, it should be noted that 31.25 subscriptions were left when y=5.
How to calculate the valueFrom the information, Saleema was investigating the newspaper subscriptions for her local newspaper. At the beginning of the year, She noted 1000 subscriptions for Subscribed to the newspaper
To find the approximate number of subscriptions left when y=5, we can substitute y=5 into the function N(y) = 1000 * (0.5)^y and evaluate it.
N(5) = 1000 * (0.5)^5
N(5) = 1000 * (0.5)^(5)
N(5) = 1000 * (0.03125)
N(5) ≈ 31.25
Approximately 31.25 subscriptions were left when y=5.
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Which expressions are equivalent to the expression 3x2 - 5a3+2y4?
Answer: There are several expressions that are equivalent to the given expression 3x^2 - 5a^3 + 2y^4. Here are a few examples:
2y^4 - 5a^3 + 3x^2-5a^3 + 3x^2 + 2y^43x^2 + 2y^4 - 5a^32y^4 + 3x^2 - 5a^3
These expressions have the same terms but may differ in the order in which the terms are written. It's important to note that the coefficients and exponents of the variables remain unchanged in each expression.
A jogger running around a rectangular park takes a shortcut back to his car by running 53 meters from one corner to the opposite corner. If the park is 45 meters long, what is the width?
Answer:
28 meters Aprox
Step-by-step explanation:
To find the width of the rectangular park, we can use the Pythagorean theorem. The diagonal running from one corner to the opposite corner forms a right triangle with the length and width of the park.
Given:
Length of the park (L) = 45 meters
Diagonal distance (d) = 53 meters
Using the Pythagorean theorem:
d² = L² + W²
(53 meters)² = (45 meters)² + W²
2809 = 2025 + W²
W² = 2809 - 2025
W² = 784
Taking the square root of both sides:
W ≈ √784
W ≈ 28
Therefore, the width of the rectangular park is approximately 28 meters.
Write a quadratic equation whose roots are 5 + i radical 2 and 5 – i radical 2
____ x^2 + _____ x+ ______=0
The quadratic equation with roots 5 + i√2 and 5 - i√2 is:
x^2 - 10x + 27 = 0
To write a quadratic equation with roots 5 + i√2 and 5 - i√2, we can use the fact that complex roots occur in conjugate pairs. Therefore, the equation will have the form:
(x - root1)(x - root2) = 0
Substituting the given roots:
(x - (5 + i√2))(x - (5 - i√2)) = 0
Now, we expand the equation:
(x - 5 - i√2)(x - 5 + i√2) = 0
Using the difference of squares formula:
((x - 5)^2 - (i√2)^2) = 0
Simplifying the equation:
(x - 5)^2 + 2 = 0
Expanding the square:
x^2 - 10x + 25 + 2 = 0
Combining like terms:
x^2 - 10x + 27 = 0
Therefore, the quadratic equation with roots 5 + i√2 and 5 - i√2 is:
x^2 - 10x + 27 = 0
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d) Suppose you begin making a monthly payment of $75.00. Fill in the table.
Month Current balance
1
2
3
4
5
6
7
8
9
10
11
12
WYPIE
$2750.00
Interest
$45.38
Payment
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
Amount applied to principal
$29.62
Answer:
Step-by-step explanation:
Answer:
For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.
For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.
Point of view:
Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!
:)
A rectangles field is 135 meters long and 100 meters wide give the length and width of another rectangular field that has the same perimeter but a larger area
Answer: if the length of the second rectangular field is 200 meters, the width should be 35 meters to have the same perimeter but a larger area.
Step-by-step explanation:
STEP1:- Let's denote the length of the second rectangular field as L2 and the width as W2.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width).
For the first rectangular field with length L1 = 135 meters and width W1 = 100 meters, the perimeter is:
Perimeter1 = 2(135 + 100) = 470 meters.
STEP 2:- To find the length and width of the second rectangular field with the same perimeter but a larger area, we need to consider that the perimeters of both rectangles are equal.
Perimeter1 = Perimeter2
470 = 2(L2 + W2)
STEP 3 :- To determine the larger area, we need to find the corresponding length and width. However, there are multiple solutions for this problem. We can set an arbitrary value for one of the dimensions and calculate the other.
For example, let's assume the length of the second rectangular field as L2 = 200 meters:
470 = 2(200 + W2)
470 = 400 + 2W2
2W2 = 470 - 400
2W2 = 70
W2 = 35 meters
HENCE L2 = 200 meters and W2 = 35 meters
April can buy a package of 10 folders for $1.20 or a package of 8 folders for $1.12. What is the unit price, per folder, in each package?
Each folder in the package of 10 costs $
Each folder in the package of 8 costs $
Answer:
Step-by-step explanation:
For the package of 10 folders: Unit price = $1.20 / 10 = $0.12 For the package of 8 folders: Unit price = $1.12 / 8 = $0.14
What is the value of x? Round to the nearest thousandth.
Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:
tan (∅) = opposite/adjacent
We have the following:
Reference angle (∅) = 53 degrees
Length of opposite side = 21
Length of adjacent side = x
Plug in the values:
tan 53 = 21/x
x * tan 53 = 21
x = 21 / tan 53
x = 15.824
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Use a table of values to graph the following exponential function. (see attachment)
y= 2^x
Please graph
By using the table of values, a graph of the exponential function is shown in the image below.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.Based on the information provided above, we can logically deduce the following exponential function;
[tex]y = 2^x[/tex]
Next, we would create a table of values based on the exponential function;
when x = 0, the y-value is given by;
y = 2⁰
y = 1
when x = 1, the y-value is given by;
y = 2¹
y = 2
x y____
-2 0.25
-1 0.5
0 1
1 2
2 4
Read more on exponential functions here: brainly.com/question/28246301
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