Answer:
A. 0 = 2x2 – 7x – 9C. 0 = 4x2 – 3x – 1D. 0 = x2 – 2x – 8Quadratic equations will have two real number solutions that are
A. 0 = 2x2 – 7x – 9
C. 0 = 4x2 – 3x – 1
D. 0 = x2 – 2x – 8
What are quadratic equations and examples?In a quadratic equation, the variable x is an unknown value, for which we need to find the solution. Examples of quadratic equations are: 6x² + 11x – 35 = 0, 2x² – 4x – 2 = 0, 2x² – 64 = 0, x² – 16 = 0, x² – 7x = 0, 2x² + 8x = 0 etc.
How do you solve quadratic equations?Solving Quadratic Equations
Put all terms on one side of the equal sign, leaving zero on the other side.Factor.Set each factor equal to zero.Solve each of these equations.Check by inserting your answer in the original equation.Learn more about quadratic equations here: https://brainly.com/question/8649555
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A rectangular page is to contain 24 sq. in. of print. The margins at the top and bottom of the page are each 1.5 inches. The margins on each side are 1 inch. What should the dimensions of the page be so that the least amount of paper is used
Answer:
Dimensions of page should be width of 6 inches and height of 9 inches
Step-by-step explanation:
Let x be the width of the printed part in inches
Let y be height of the printed part in inches.
Thus, Area of printed part; A = xy
And area of printed part is given as 24.
Thus, xy = 24
Making y the subject, we have;
y = 24/x
Now, the question says the top and bottom margins are 1.5 inches.
Thus, width of page = x + 1 + 1 = x + 2
And also the margins on each side are both 1m in length, thus the height of page will be:
y + 1.5 + 1.5 = y + 3
So area of page will now be;
A = (x + 2)•(y+3)
From earlier, we got y = 24/x
Thus,plugging this into area of page, we have;
A = (x + 2)•((24/x)+3)
A = 24 + 3x + 48/x + 6
A = 30 + 3x + 48/x
For us to find the minimum dimensions, we have to find the derivative of A and equate to zero
Thus,
dA/dx = 3 - 48/x²
Thus, dA/dx = 0 will be
3 - 48/x² = 0
Multiply through by x²:
3x² - 48 = 0
Thus,
3x² = 48
x² = 48/3
x = √16
x = 4 inches
Plugging this into y = 24/x,we have;
y = 24/4 = 6 inches
We want dimensions of page at x = 4 and y = 6.
From earlier, width of page = x + 2.
Thus,width = 4 + 2 = 6 inches
Height = y + 3 = 6 + 3 = 9 inches
So dimensions of page should be width of 6 inches and height of 9 inches
To minimize paper usage, we need to find the dimensions of the rectangular page. By setting up an equation and solving it, we can find the width and length of the page that result in the least amount of paper used.
Explanation:To minimize the amount of paper used, we need to find the dimensions of the page that will result in the smallest possible area. Let's assume the length of the page is 'L' inches and the width is 'W' inches. We can set up the equation:
Next, we can use the quadratic formula to solve for L:
To find the minimum value of L, we can consider the factors contributing to the uncertainty:
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Sally has $21.40 in dimes and quarters. There are 100 coins in all. How many of each coin does she have?
x = dimes
y = quarters
We also know:
Dimes: 0.10
Quarters: 0.25
100 = x + y
So, 0.10x + 0.25y = 100
And, y = 100 - x
Let’s use substitution:
0.10x + 0.25( 100 - x ) = 100
= 0.10x + 25 - 0.25x = 100
= 25 - 100 = 0.25x - 0.10x
= (-75) = 0.15x
x = (-75) divide by 0.15
x = (-500)
Two of the steps in the derivation of the quadratic
formula are shown below.
Which operation is performed in the derivation of the
quadratic formula moving from Step 6 to Step 7?
subtracting bi from both sides of the equation
Step 6: barangan = (x +
Step 7: tvb22400 = x +
squaring both sides of the equation
taking the square root of both sides of the equation
taking the square root of the discriminant
Please help quick
Answer:
a
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
taking the square root of both sides of the equation
What percentage of the data values falls between the values of 3 and 24 in the data set shown?
A box-and-whisker plot. The number line goes from 0 to 25. The whiskers range from 3 to 24, and the box ranges from 6 to 19. A line divides the box at 15.
Answer
25 percent
Step-by-step explanation:
Answer:
The correct answer is 100%
Step-by-step explanation:
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An open-top bin is to be made from a 15-centimeter by 40-centimeter piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What size square should be cut out of each corner to get a bin with the maximum volume?
No squares should be cut. Maximum volume is zero. Dimensions remain 15cm by 40cm by 0cm.
To find the size of the square that should be cut out from each corner to maximize the volume of the bin, we need to follow these steps:
1. Understand the problem : We have a rectangular piece of plastic with dimensions 15 cm by 40 cm. By removing squares from each corner and folding up the flaps, we can form an open-top bin. We want to find the size of the squares to be cut out to maximize the volume of the bin.
2. Define variables : Let's denote the side length of the square to be cut out from each corner as [tex]\( x \)[/tex] cm.
3. Express the volume of the bin : After cutting out squares and folding up the flaps, the dimensions of the resulting bin will be [tex]\( (15 - 2x) \)[/tex] cm by [tex]\( (40 - 2x) \)[/tex] cm by [tex]\( x \)[/tex] cm. So, the volume of the bin can be expressed as: [tex]\[ V = x(15 - 2x)(40 - 2x) \][/tex]
4. Maximize the volume: To find the maximum volume, we need to find the critical points of the function [tex]\( V \)[/tex]. We'll take the derivative of [tex]\( V \)[/tex] with respect to [tex]\( x \)[/tex], set it equal to zero, and solve for [tex]\( x \)[/tex].
[tex]\[ \frac{dV}{dx} = (15 - 2x)(40 - 2x) + x(-4)(40 - 2x) + x(15 - 2x)(-4) \][/tex]
[tex]\[ 0 = (15 - 2x)(40 - 2x) - 8x(40 - 2x) - 4x(15 - 2x) \][/tex]
5. Solve for [tex]\( x \)[/tex] : Solve the equation for [tex]\( x \)[/tex] to find the critical points.
[tex]\[ 0 = 600 - 70x + 4x^2 \][/tex]
[tex]\[ 0 = 4x^2 - 70x + 600 \][/tex]
Solve for [tex]\( x \)[/tex] using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where [tex]\( a = 4 \)[/tex], [tex]\( b = -70 \)[/tex], and [tex]\( c = 600 \)[/tex].
[tex]\[ x = \frac{-(-70) \pm \sqrt{(-70)^2 - 4(4)(600)}}{2(4)} \][/tex]
[tex]\[ x = \frac{70 \pm \sqrt{4900 - 9600}}{8} \][/tex]
[tex]\[ x = \frac{70 \pm \sqrt{-4700}}{8} \][/tex]
Since the discriminant is negative, there are no real solutions for [tex]\( x \)[/tex] in this case. Therefore, we need to check the endpoints of our interval.
6. Check endpoints : Since [tex]\( x \)[/tex] must be non-negative and [tex]\( (15 - 2x) \)[/tex] and [tex]\( (40 - 2x) \)[/tex] must also be positive, the possible range for [tex]\( x \)[/tex] is [tex]\( 0 \leq x \leq 7.5 \)[/tex] cm.
When [tex]\( x = 0 \), \( V = 0 \)[/tex] (no bin is formed).
When [tex]\( x = 7.5 \), \( V = 7.5(15 - 2(7.5))(40 - 2(7.5)) = 7.5(0)(25) = 0 \)[/tex] (no bin is formed).
7. Conclusion : The maximum volume of the bin is achieved when no squares are cut out from the corners. Therefore, to maximize the volume, no squares should be cut out from the corners of the plastic, resulting in a rectangular prism with dimensions [tex]\( 15 \times 40 \times 0 \)[/tex] cm³, which does not form a bin.
So, the maximum volume of the bin is [tex]1000cm^3[/tex]
To maximize the volume of the bin, we need to determine the dimensions of the squares that should be cut out from each corner to form the bin. Let's denote the side length of the square to be cut out as
x centimeters.
When the squares are cut out and the flaps are folded up, the dimensions of the resulting bin can be expressed as follows:
Length of the bin: 40−2x centimeters
Width of the bin: 15−2x centimeters
Height of the bin (equal to the side length of the square cut out): x centimeters
The volume V of the bin is given by the product of its length, width, and height:
V=(40−2x)(15−2x)x
To find the maximum volume, we need to find the value of
x that maximizes this function. We can do this by taking the derivative of
V with respect to x, setting it equal to zero, and solving for x.
Let's find the derivative of V with respect to x:
[tex]$\frac{d V}{d x}=15(40-2 x)-2(15-2 x)(40-2 x)$[/tex]
Now, let's set the derivative equal to zero and solve for x:
[tex]$15(40-2 x)-2(15-2 x)(40-2 x)=0$[/tex]
After solving for x, we can substitute the value of
x back into the expression for the volume
V to find the maximum volume of the bin. Let's do these calculations.
First, let's simplify the derivative[tex]\frac{dv}{dx}[/tex]
[tex]$\begin{aligned} & \frac{d V}{d x}=15(40-2 x)-2(15-2 x)(40-2 x) \\ & =600-30 x-\left(30 x-4 x^2\right) \\ & =600-30 x-30 x+4 x^2 \\ & =600-60 x+4 x^2\end{aligned}$[/tex]
Now, we set the derivative equal to zero and solve for x:
[tex]$600-60 x+4 x^2=0$[/tex]
Dividing both sides by 4:
[tex]$150-15 x+x^2=0$[/tex]
Rearranging and factoring:
[tex]$$\begin{aligned}& x^2-15 x+150=0 \\& (x-10)(x-15)=0\end{aligned}$$So, $x=10$ or $x=15$.[/tex]
Since x=15 would result in a negative side length for the bin, we discard it.
Thus, the optimal size square to be cut out from each corner is 10 centimeters.We can then find the maximum volume
V by substituting x=10 into the volume formula:
[tex]$V=(40-2 \times 10)(15-2 \times 10) \times 10=(20)(-5) \times 10=1000 \mathrm{~cm}^3$[/tex]
So, the maximum volume of the bin is [tex]1000cm^3[/tex]
The radius of a circle is (7x+3)cm. Write an expression to represent the area of the circle in simplified form
Answer:
A = π(7x + 3)² cm²
Step-by-step explanation:
A = πr² is the appropriate equation. If r = 7x + 3 cm, then the area of this particular circle is:
A = π(7x + 3)² cm²
Final answer:
The area of a circle with radius (7x+3)cm is represented by the simplified expression 49x²π + 42xπ + 9π square centimeters.
Explanation:
To find the area of a circle with radius (7x+3)cm, we use the formula for the area of a circle, which is A = πr². So, substituting the given radius into this formula, we get:
A = π(7x+3)²
To simplify the expression, we square the binomial:
A = π(49[tex]x^2[/tex] + 42x + 9)
Therefore, the area of the circle in simplified form is 49[tex]x^2[/tex]π + 42xπ + 9π square centimeters.
A company has been rating television programs for more than 60 years. It uses several sampling procedures, but its main one is to track the viewing patterns of 20,000 households. These contain more than 45,000 people and are chosen to form a cross-section of the overall population. The households represent various locations, ethnic groups, and income brackets. The data gathered from the sample of 20,000 households are used to draw inferences about the population of all households in the United States. Complete parts (a) and (b) below. What strata are used in the sample? Choose the correct answer below.
A. The various locations, ethnic groups, and income brackets that are represented
B. The various sampling procedures and viewing patterns
C. The number of households and people that are chosen
D. The television ratings
Why is it important to have a stratified sample for these ratings? Choose the correct answer below.
A. Stratified sampling ensures that all of the members of one or more groups are used.
B. Stratified sampling ensures that the television ratings are accurate.
C. Stratified sampling ensures that each segment of the population is represented.
D. Stratified sampling ensures that only households in the U.S. are sampled
Using stratified sampling concepts, it is found that the correct options are:
A. The various locations, ethnic groups, and income brackets that are representedC. Stratified sampling ensures that each segment of the population is represented.Stratified sampling divides the population into groups, called stratas, and a few elements of each group are surveyed.
In this problem, the households are divided to represents various locations, ethnic groups, and income brackets, hence, those are the stratas.
Stratified sampling is used because ensures that all segments of the population are represented.
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f the angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree, what is the height of the tree (to the nearest tenth of a foot)?
A) 14.0 feet
B) 16.9 feet
C) 19.3 feet
D) 20.7 feet
Given:
The angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree.
We need to determine the height of the tree.
Height of the tree:
Let the height of the tree be h.
The height of the tree can be determined using the trigonometric ratio.
Thus, we have;
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
Substituting the values, we get;
[tex]tan \ 34^{\circ}=\frac{h}{25}[/tex]
Multiplying both sides by 25, we have;
[tex]tan \ 34^{\circ} \times 25=h[/tex]
[tex]0.6745 \times 25=h[/tex]
[tex]16.8625=h[/tex]
Rounding off to the nearest tenth of a foot, we get;
[tex]16.9=h[/tex]
Thus, the height of the tree is 16.9 feet.
Hence, Option B is the correct answer.
Correct option is B. The height of the tree can be found using the tangent of the angle of elevation, which is the ratio of the tree's height to the distance from the base. Applying the formula, the height is approximately 16.9 feet, matching option B.
To calculate the height of the tree given the angle of elevation and the distance from the point on the ground to the base of the tree, we can use trigonometric functions, specifically the tangent function in a right triangle. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the point on the ground to the tree).
Using the formula:
tangent(angle) = opposite / adjacent
Substitute the given values:
tangent(34°) = height of the tree / 25 ft
Now solve for the height:
height = 25 ft * tangent(34°)
Use a calculator to find:
height = 25 ft * 0.6745
height = 16.9 ft
Therefore, the height of the tree is approximately 16.9 feet (to the nearest tenth of a foot), making option B the correct answer.
What is the volume of the prism shown below?
A rectangular prism with length of 6 inches, height of 7 inches, and width of 3 inches.
16 cubic inches
21 cubic inches
90 cubic inches
126 cubic inches
Answer:
The answer is 126!!! Hope I helped!!!
Step-by-step explanation:
1. 6 x 3 = 18
2. 18 x 7 = 126
Answer:
126
Step-by-step explanation:
Multiply 7 x 6 x 3 which is equal to 126.
Have a great day! Your amazing. I do a lot of answers on edg 6th grade.
Feel free to ask questions
Ahmed was studying the shapes of quartz crystals, one of which he outlined below.
A figure can be broken into a parallelogram and triangle. The parallelogram has a base of 3 feet and height of 5 feet. The triangle has a base of 3 feet and height of 2 feet.
What is the area of the quartz crystal he was studying, in square feet?
Feet squared
Answer:
The answer is 18 feet squared
Step-by-step explanation:
Answer:
The answer is 18 ft squared
Step-by-step explanation:
i just got 100% i know all the right answers
Add 3 to x, double what you have, then subtract 1 from the result
Answer:
-6
Step-by-step explanation:
3x * 2 = 6x - 1 = -6
The required result of the given expression is 2x - 5.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
Add 3 to x, double what you have, then subtract 1
So, we can write,
Add 3 to x = 3 + x
Double = 2(3 + x)
Subtract from = 1 - 2(3 + x)
Simplifying we get,
1 - 6 + 2x
solving we get,
1 - 6 + 2x = 2x - 5
this is the required result.
Thus, the required result of the given expression is 2x - 5.
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The radius of the water bottle is about _______cm.
Answer:
45.216
Step-by-step explanation:
2 x 3.14 x7.2
Answer:
Step-by-step explanation:
Volume of water bottle = 143 cubic cm
πr²h = 143
3.14*r²*7.2 = 143
[tex]r^{2}=\frac{143}{3.14*7.2}\\\\r^{2}=6.325\\[/tex]
r = 2.51
r = 2.5 cm
Simplify the trigonometric function
Answer:
a. csc²θ
Step-by-step explanation:
You can use the identities ...
1 +tan² = sec²
cot = cos/sin
sec = 1/cos
csc = 1/sin
___
Then the expression becomes ...
[tex]\cot^2{\theta}(1+\tan^2{\theta})=\cot^2{\theta}\sec^2{\theta}=\dfrac{\cos^2{\theta}}{\sin^2{\theta}\cos^2{\theta}}=\dfrac{1}{\sin^2{\theta}}\\\\=\boxed{\csc^2{\theta}}[/tex]
A theme park ride has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumference of 521.24 yd. What is the surface area of the sphere? Use 3.14
Answer:
The surface area of the sphere is 86525.84 square yards
Step-by-step explanation:
The widest circle of the sphere has the same radius of the sphere
Use the circumference of the circle to find its radius, then use it to find the surface area of the sphere
The formula of the circumference of the circle is C = 2π r
The formula of the surface area of the sphere is SA = 4π r²
∵ The circumference of the widest circle is 521.24 yards
∴ C = 521.24
- Equate the formula of the circumference by it
∴ 2π r = 521.24
∵ π ≈ 3.14
∴ 2(3.14) r = 521.24
∴ 6.28 r = 521.24
- Divide both sides by 6.28
∴ r = 83 yards
Now use the formula of the surface area of the sphere to find it
∵ The radius of the sphere = the radius of the widest circle
∴ The radius of the sphere is 83 yards
∵ SA = 4π r²
- Substitute r by 83 and π by 3.14
∴ SA = 4(3.14)(83)²
∴ SA = 86525.84
The surface area of the sphere is 86525.84 square yards
what is the probability of tossing at least 1 tail of you toss 3 coins at once
Explanation: Probability of NOT getting a tail in 3 coin toss is (12)3=18 . Probability of getting at least 1 tail in 3 coin toss is 1−18=78
Can three segments with length 4 cm 6 cm and 11 cm be assembled to form an acute triangle a right triangle or an obtuse triangle?
Final answer:
Three segments with lengths 4 cm, 6 cm, and 11 cm cannot form a triangle because the sum of the lengths of the two shorter sides is not greater than the length of the longest side, violating the Triangle Inequality Theorem.
Explanation:
To determine whether three segments with lengths 4 cm, 6 cm, and 11 cm can form a triangle, we must consider the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. If we attempt to apply this to the given lengths:
4 cm + 6 cm > 11 cm (False)
4 cm + 11 cm > 6 cm (True)
6 cm + 11 cm > 4 cm (True)
Since the sum of the lengths of the two shorter sides (4 cm + 6 cm) is not greater than the length of the longest side (11 cm), these three segments cannot form a triangle, whether it is an acute triangle, right triangle, or obtuse triangle.
If they were able to form a triangle, to classify the type of triangle, we would use the Converse of the Pythagorean Theorem. This theorem helps us understand if a triangle is acute, right, or obtuse:
In a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.
If the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse.
If the square of the longest side is less than the sum of the squares of the other two sides, the triangle is acute.
However, since a triangle cannot be formed with these segments, we do not need to apply these rules here
Which is equivalent to log Subscript 2 Baseline n = 4?
A)log n = StartFraction log 2 Over 4 EndFraction
B)n = StartFraction log 2 Over log 4 EndFraction
C)n = log 4 times log 2
D)log n = 4 log 2
Answer:
D) log n = 4 log 2Step-by-step explanation:
Given
log₂ n = 4Compare the given with the options to identify equivalents
A)
log n = log 2 / 4 log₂ n / log₂ 10 = 1/ log₂ 10 ÷ 4log₂ n = 1/4Not equivalent
B)
n = log 2 / log 4n log 4 = log 2n log₂ 4 / log₂ 10 = 1 / log₂ 10n log₂ 4 = 1Not equivalent
C)
n = log 4 × log 2n = log₂ 4/ log₂ 10 × 1/ log₂ 10n = 2 /(log₂ 10)²n (log₂ 10)² = 2Not equivalent
D)
log n = 4 log 2log₂ n / log₂ 10 = 4 × 1/log₂ 10log₂ n = 4Equivalent
The model of a new apartment building have dimensions of 10 inches in width, 18 inches in length and 28 inches in height. The architect plans for the building to be 144 times the dimensions of the model. What will be the volume and surface area or the new building when it is completed?
The volume of the new building is 11,726,069,760 cubic inches, and its surface area is 51,555,840 square inches.
To find the volume and surface area of the new building, we first need to calculate the dimensions of the new building by scaling up the dimensions of the model by a factor of 144.
1. Dimensions of the new building:
-[tex]Width: \(10 \times 144 = 1440\) inches[/tex]
- [tex]Length: \(18 \times 144 = 2592\) inches[/tex]
- [tex]Height: \(28 \times 144 = 4032\) inches[/tex]
2. Volume of the new building:
The volume of a rectangular prism (building) is calculated by multiplying its length, width, and height.
[tex]\[Volume = \text{Length} \times \text{Width} \times \text{Height}\][/tex]
Substituting the given dimensions:
[tex]\[Volume = 2592 \times 1440 \times 4032\][/tex]
[tex]\[Volume = 11,726,069,760 \text{ cubic inches}\][/tex]
3. Surface area of the new building:
The surface area of a rectangular prism (building) is calculated by adding the areas of all six sides.
[tex]\[Surface\,Area = 2(\text{Length} \times \text{Width} + \text{Length} \times \text{Height} + \text{Width} \times \text{Height})\][/tex]
Substituting the given dimensions:
[tex]\[Surface\,Area = 2(2592 \times 1440 + 2592 \times 4032 + 1440 \times 4032)\][/tex]
[tex]\[Surface\,Area = 51,555,840 \text{ square inches}\][/tex]
So, when the new building is completed:
- The volume will be [tex]\(11,726,069,760 \text{ cubic inches}\).[/tex]
- The surface area will be [tex]\(51,555,840 \text{ square inches}\).[/tex]
17 points! Which system of equations has an infinite number of solutions?
2x – 6y = 18
x – y = 9
2x – 6y = 18
x + 3y = 9
2x – 6y = 18
x – 3y = 9
Answer:
The bottom equation is infinite solutions ( please give branliest)
2x - 6y = 18
x - 3y = 9
Step-by-step explanation:
Using substitution,
x=3y + 9
6x - 6x + 18 = 18
0 = 18 - 18
0 = 0
Answer: Last one:)
Step-by-step explanation:
Just did it
14x – 2y = 1
2x - Y= -2
A fertiliser is produced by mixing water and pesticide in the ratio of 9:3. The final quantity of fertiliser is 48 litres. What is the quantity of water and pesticide that is needed?
Answer:
Step-by-step explanation:
9 + 3 = 12
[tex]Water=\frac{9}{12}*48\\\\=9*4[/tex]
Water = 36 liters
Pesticide = 48 - 36 = 12 liters
Maria is making a candle in the shape of a cylinder. She wants the candle to have a height of 3 cm and a radius of 2 cm. How much wax does Maria need?
12 cm3
12 cm2
18 cm3
20 cm2
Answer:
V(cylinder) = πr²h
h=3 cm
r=2 cm
V(cylinder) = πr²h = π*2²*3 =12π cm³
Answer : 12π cm³.
Answer:
A
Step-by-step explanation:
12π cm³
Micah recorded the amount of time his mom and dad spend reading bedtime stories. He plotted the data in the box plot below.
A box plot titled Minutes mom spends reading. The number line goes from 10 to 25. The whiskers range from 13 to 25, and the box ranges from 15 to 19. A line divides the box at 16.
Minutes Mom Spends Reading
A box plot titled Minutes dad spends reading. The number line goes from 10 to 25. The whiskers range from 11 to 19, and the box ranges from 12 to 15. A line divides the box at 13.
Minutes Dad Spends Reading
Which is an accurate comparison of the two data sets?
The lengths of time that his mom reads are typically longer and have less variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically shorter and have less variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically shorter and have more variability than the lengths of time that his dad reads.
Answer:
The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.
Step-by-step explanation:
The Mom's plot is longer in ranges, therefore, she would have more variability than the dad.
Answer:
B
Step-by-step explanation:
The top of the chimney needed to be replaced. The new top for the chimney will cost $800 plus $40 per hour for labor. If it took the chimney guy 75 minutes to complete the work, how much will Mrs. Bredice pay?
Answer:
Step-by-step explanation:
suppose ACT Mathematics scores are normally distributed with a mean of 21.3 and a standard deviation of 5.3. A university plans to send letters of recognition to students whose scores are in the top 11%. What is the minimum score required for a letter of recognition
Answer: the minimum score required for a letter of recognition is 27.8
Step-by-step explanation:
Suppose ACT Mathematics scores are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = ACT Mathematics scores.
µ = mean score
σ = standard deviation
From the information given,
µ = 21.3
σ = 5.3
The probability of students whose scores are in the top 11 % would be be (1 - 11/100) = (1 - 0.11) = 0.89
Looking at the normal distribution table, the z score corresponding to the probability value is .23
Therefore,
1.23 = (x - 21.3)/5.3
Cross multiplying by 8.6, it becomes
1.23 × 5.3 = x - 21.3
6.519 = x - 21.3
x = 6.519 + 21.3
x = 27.8 to the nearest whole number
Final answer:
The minimum ACT Mathematics score required to be in the top 11% with a mean of 21.3 and a standard deviation of 5.3 is approximately 27.85, which is usually rounded to 28.
Explanation:
Top 11% for ACT Mathematics Score Requirement
If ACT Mathematics scores are normally distributed with a mean of 21.3 and a standard deviation of 5.3, the score corresponding to the top 11% can be found by determining the z-score that corresponds to the 89th percentile (100% - 11% = 89%). To find this z-score, one would typically use a z-score table or a statistical software. Once the z-score for the 89th percentile is found, it can be converted to an ACT score using the formula:
Z = (X - μ) / σ
where Z is the z-score, X is the ACT score, μ (mu) is the mean, and σ (sigma) is the standard deviation. Solving for X:
X = Z×σ + μ
Assuming the z-score for the 89th percentile is approximately 1.23, the minimum required score for a letter of recognition would be:
X = 1.23×5.3 + 21.3
X ≈ 1.23×5.3 + 21.3
X ≈ 6.549 + 21.3
X ≈ 27.849
Therefore, the minimum score required for a letter of recognition would be approximately 27.85, which can be rounded as appropriate for the context (usually to the nearest whole number, giving a score of 28).
The sum of three consecutive numbers is one hundred thirty - eight.
What is the smallest of the three numbers
Answer:
45
Step-by-step explanation:
The average of the three numbers is the middle one: 138/3 = 46. Then the smallest of the three consecutive numbers is 45.
Final answer:
The smallest of the three consecutive numbers that add up to 138 is 45.
Explanation:
To find the smallest of the three consecutive numbers that add up to one hundred thirty-eight, we first need to represent the numbers algebraically.
Let x be the smallest number, x+1 is the next number, and x+2 is the largest number.
The equation that represents their sum is:
x + (x + 1) + (x + 2) = 138
To solve for x, we combine like terms:
3x + 3 = 138
Then we subtract 3 from both sides:
3x = 135
And divide both sides by 3 to find x:
x = 135 / 3
x = 45
Therefore, the smallest number is 45.
A racecar can go round the track 48 times in 8 minutes how many times can it go around the track per minute
Answer:
6 times
Step-by-step explanation:
48/8=6
Answer: 10 seconds for one time around the track.
Step-by-step explanation:
48 times=8 minutes
1 time= 8/48
8/48=4/24
4/24=2/12
1/6. 1/6 of a minute equals 10 seconds.
The answer is 10 seconds
Are the following two matrices inverses of one
another? (Urgent please help)
A=[ 4 2] B= [ -4 -2]
[-11 -6] [ 11 7]
a)Yes, because they are opposites.
b)Yes, because their product is equal to the
identity matrix
c)No, because they are not opposites.
d)No because their product is not equal to the matrix
Answer: D
Step-by-step explanation:
The correct answer is d) No because their product is not equal to the identity matrix.
The matrices are given in the question as follows:
[tex]A= \left[\begin{array}{ccc}4&2\\-11&-6\end{array}\right] \\B= \left[\begin{array}{ccc}-4&-2\\11&6\end{array}\right][/tex]
To determine if two matrices are inverses of each other, we need to check if their product is equal to the identity matrix.
Let's calculate the product of matrices A and B:
[tex]A{\times}B = \left[\begin{array}{ccc}4\times-42+2\times11&4\times-2+2\times6\\-11\times-4+(-6\times11)&-11\times-2-6\times6\end{array}\right][/tex]
Simplifying the calculations to get:
[tex]A{\times}B = \left[\begin{array}{ccc}6&4\\-22&-14\end{array}\right][/tex]
The resulting matrix is not equal to the identity matrix:
[tex]A{\times}B = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Therefore, matrices A and B are not inverses of each other.
The correct answer is d) No because their product is not equal to the identity matrix.
To learn more about the matrix click here:
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What are the coordinates of point C of the directed segment from A(-8,4) to B(10,-2) that partitions the segment such that AC:CB is 2:1?
Final answer:
To find the coordinates of point C that partitions the segment from A(-8,4) to B(10,-2) in the ratio 2:1, we use the formula for internal division of a line segment, resulting in the coordinates (4, 0).
Explanation:
The coordinates of point C that partitions the segment from A(-8,4) to B(10,-2) in the ratio 2:1 can be found using the formula for internal division of a line segment. Since AC:CB is 2:1, we consider the section ratio to be 2/3 and multiply it by the difference in the corresponding x and y coordinates of A and B, then add to the coordinates of point A.
The x-coordinate of point C is calculated as follows:
Cx = Ax + (Bx - Ax) * m/(m+n)
Where Ax is the x-coordinate of point A, Bx is the x-coordinate of point B, and m/n is the ratio (2/1 in this case), so m=2 and n=1.
Cx = (-8) + (10 - (-8)) * 2/(2+1) = -8 + 18 * 2/3 = -8 + 12 = 4
The y-coordinate of point C is calculated similarly:
Cy = Ay + (By - Ay) * m/(m+n)
Cy = 4 + ((-2) - 4) * 2/(2+1) = 4 + (-6) * 2/3 = 4 - 4 = 0
Thus, the coordinates of point C are (4, 0).
Each month. Diana donates the same amount of money to a charity. If she donates 1,500 in one year, how much does she donate each month?
Answer: $125
Step-by-step explanation:
1500/12=125