The two positive numbers satisfying the given requirements are 15.56 and 15.56
For given question,
Let x and y be two positive numbers satisfying the given requirements.
⇒ xy = 242 .............(1)
The sum of given two positive numbers is a minimum.
Let the sum of given two positive numbers is S.
⇒ x + y = S ............(2)
From equation(1),
⇒ y = 242/x
Substitute above value of y in equation (2),
⇒ x + y = S
⇒ S = x + (242 / x)
Now, for above equation we find the derivative of x with respect to x.
⇒ 0 = 1 - [tex]\frac{242}{x^{2} }[/tex]
⇒ 242/x² = 1
⇒ x² = 242
⇒ x = ±15.56
Since the numbers are positive, x = 15.56
For x = 15.56
⇒ y = 15.56
Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56
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3. What is the missing term in the sequence below?
3, 6, 11, ?, 27, 38, 51
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 241(1.06) t. the variable t represents the number of years since 2000. what is the projected annual percent of growth, and what should the company be worth in 2011?
Answer:
6%- 457 Million
Step-by-step explanation:
w=241(1.06)^11=457 million
Part A: Write an algebraic expression for 6 more than 7 times a number. (5 points)
Part B: Write a verbal expression for 3(n + 8). (5 points)
The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".
Linear ExpressionA linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.
Part AFirst, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.
The word more will be represented for the add symbol (+). Thus,
the algebraic expression is 6+7x.
Part BThe expression 3*(n+8) can be represented for the sentence:
The triple of the sum between the numbers n and 8.
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27. Write down the co-ordinates of the points where the line y = 4x - 3 cuts the x-axis
Step-by-step explanation:
it is a line, so that is 1 point, where it cuts the x-axis.
in general that means y = 0.
so,
0 = 4x - 3
4x = 3
x = 3/4
the point, where the line cuts the x-axis is
(3/4, 0)
In the circle below, AB is a diameter. Suppose stack CB equals 32 degrees and m angle B C D equals 52 degrees.
Find the following. Type your numerical answers (without units) in each blank.
The 32° measure of arc CB, and m<BCD which is 52° gives m<BAC and m<ACB as 16° and 90° respectively, from which we have;
m<CBA = 74°m<ACD = 38°Which circle theory can be used to find the required angles?First part;
Given;
Angle subtended by arc CB = 32°
m<BCD = 52°
Based on circle theory, we have;
Angle subtended by an arc at the center of a circle is twice the angle subtended at the circumferenceTherefore;
Arc CB = 2 × m<BAC
Which gives;
Arc CB = 32° = 2 × m<BAC
m<BAC = 32° ÷ 2 = 16°
Angle subtended by the diameter at the circumference is 90°.
Therefore;
m<ACB = 90°
In triangle ∆ABC, we have;
m<ACB + m<BAC + m<CBA = 180°
m<CBA = 180° - (m<ACB + m<BAC)
Therefore;
m<CBA = 180° - (90° + 16°)
m<CBA = 180° - (90° + 16°) = 74°
m<CBA = 74°Second part;
The arc subtending m<ACD is AB which is also the diameter.
Angle formed by the diameter, which is a straight line = 180°
Therefore;
Angle subtended at the center by arc AB = 180°
Angle subtended at the circumference, m<ACB is therefore;
m<ACB = 180° ÷ 2 = 90°
A
m<ACB = m<ACD + m<BCD (Angle addition property)
Therefore;
90° = m<ACD + 52°
m<ACD = 90° - 52° = 38°
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A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table shows the data:
Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31
Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indica
Answer: GET BRAINLY PLUS FOR VERIFIED ANSWERS NOW
Step-by-step explanation:
NOW
What is the domain of the function in the graph?
A. 4≤y≤6
B. 20≤y≤70
C. 4≤x≤6
D. 20≤x≤70
Answer:
C. 4≤x≤6
Step-by-step explanation:
First things first, let’s learn the difference between domain and range. Domain is the spread of the x values and range is the spread of the y values. This means that in this question, you can rule out options A and B because those could potentially show range. Now we are left with options C and D. When we look at the first x coordinate, we see that it’s a 4. The last x coordinate is a 6. This means that the domain is greater than or equal to 4, but less than or equal to 6. You can also represent it as 4≤x≤6.
Hope that helps! Have a fantastic day!
Michelle is purchasing fabric for two new sewing projects: a hat and a tote bag. The two projects each need red and black fabric. The hat requires 2 yards of red fabric and 1 yard of black fabric. The tote bag requires 2 yards of red fabric and 4 yards of black fabric. Michelle paid $14 for the hat’s fabric and $26 for the tote bag’s fabric. How much does one yard of each fabric cost?
The cost of one yard of black fabric is $4.
The cost of one yard of red fabric is $5.
What are the linear functions that represent the question?2r + b = 14 equation 1
2r + 4b = 26 equation 2
Where:
r = cost of one yard of red fabric
b = cost of one yard of black fabric
What is the cost of each type of fabric?
Subtract equation 1 from equation 2
3b = 12
b = 12 / 3
b = 4
Substitute for b in equation 1
2r + 4 = 14
2r = 14 - 4
2r = 10
r = 10 / 2
r = $5
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if 7 cosec^2 theta-9 cot^2theta=7 then what is the value of tantheta
[tex]\displaystyle\\Answer:\theta=\frac{\pi }{2}+\pi n.[/tex]
Step-by-step explanation:
[tex]\displaystyle\\7*cosec^2\theta-9*cot^2\theta=7\\7-7*cosec^2\theta+9*cot^2\theta=0\\7-\frac{7}{sin^2\theta}+9*\frac{cos^2\theta}{sin^2\theta} } =0\\\frac{7*sin^2\theta-7+9*cos^2\theta}{sin^2\theta} =0\\\frac{-7*(1-sin^2\theta)+9*cos^2\theta}{sin^2\theta} =0\\\frac{-7*cos^2\theta+9*cos^2\theta}{sin^2\theta} =0\\\frac{2*cos^2\theta}{sin^2\theta}=0\\[/tex]
[tex]2*cot^2\theta=0\\Divide\ the\ right\ and\ initial\ parts\ by\ 2:\\cot^2\theta=0\\cot\theta=0\\\theta=\frac{\pi }{2}+\pi n\ \ \ (n=0,\ 1,\ 2,\ 3\ ...).[/tex]
what is the general form of the equation for the given circle?
The general equation for a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h,k)[/tex] is the centre of the circle and [tex]r[/tex] is the radius.
Solving the QuestionFirst, we can determine the centre of the circle.
( _ , _ )
The point directly on top is (4,7). Because it lies on the same vertical line as the centre, they have the same x-coordinate.
(4, _ )
The point directly to the right of it is (7,4). Because it lies on the same horizontal line as the centre, they have the same y-coordinate.
(4,4)
Therefore, the centre of the circle is (4,4). Plug this into the general equation:
[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-4)^2=r^2[/tex]
Now, we can determine the radius of the circle.
To do this, we can calculate the distance between the centre of the circle and one of the given points that lie on the circumference.
The centre is (4,4), and one of the points is (4,7). Because they only have a difference of 3 units in the y-direction (and none in the x-direction), this means that the radius is 3 units. Plug this into the general equation:
[tex](x-4)^2+(y-4)^2=r^2\\(x-4)^2+(y-4)^2=3^2\\(x-4)^2+(y-4)^2=9[/tex]
Answer[tex](x-4)^2+(y-4)^2=9[/tex]
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
The volume of the cylinder and the cone is equal
Volume of a cylinder and a coneThe formula for calculating the volume of a cylinder is expressed as:
V = πr²h
where
r is the radius
h is the height
For the cylinder
r = 8/2 = 4 in
h = 5
Substitute
V = π(4)²*5
V = 80π cubic inches
For the cone
r = 4 in
h = 15in
Substitute
V = 1/3πr^2h
V = 1/3(π)(4)^2 * 15
V = 80π cubic inches
Hence the volume of the cylinder and the cone is equal
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Which of the following is equivalent to 1/log3(m)
Answer: A
Step-by-step explanation:
We can rewrite the expression as
[tex]\frac{\log_{3} 3}{\log_{3} m}[/tex]
Using the change of base formula, we get [tex]\log_{m} 3\[/tex]
For s=5 and t=8, 3st²-s²:
3st²-s² =
Step-by-step explanation:
Given,
s=5
t=8
solution,
= 3st² - s²
= 3*5*8² - 5²
= 3*5*64 - 25
= 960 - 25
= 935
Poisson distribution
Given that Y ~ Po(4.5)
Find y such that P(Y=y) is the greatest, for y = 0,1,2....
Ans is 4 but i dont know the steps
20 POINTS
Here are the scores of 18 students on a history test. 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89. Notice that the scores are ordered from least to greatest. Make a box-and-whisker plot for the data.
The median of this box and whisker plot is 73
A box and whisker plot is defined as a graphical method of displaying variation in a set of data. In most cases, a histogram analysis provides a sufficient display, but a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph. Box and whisker plots are very effective and easy to read, as they can summarize data from multiple sources and display the results in a single graph. Box and whisker plots allow for comparison of data from different categories for easier, more effective decision-making.
From the given data, following can be inferred
Population size: 18Median: 73Minimum: 55Maximum: 89First quartile: 61.75Third quartile: 83.5Interquartile Range: 21.75which is demonstrated in the box and whisker plot below
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Find the area of a kite with diagonal length of 10 and 25 meters.
The Area of the kite with the given diagonals is: 125 square meters.
What is a Kite?A kite can be described as a quadrilateral having four (4) sides, which can be categorized into two pairs of congruent sides, each of them is adjacent to the other. A kite has two diagonals that intersect, where by the longer diagonal divides the smaller diagonal into equal halves.
An example of a kite is shown in the image attached below, where:
JL and KM are the diagonals of the kite.
How to Find the Area of a Kite?The formula for finding the area of a kite is given as:
Area = 1/2 × (product of the lengths of the diagonals)
Given the following:
Length of diagonal 1 = 10 meters
length of diagonal 2 = 25 meters
Area = 1/2 × (product of the lengths of the diagonals) = 1/2 × (10 × 25)
Area of kite = 1/2 × (250)
Area of kite = 1/2 × (250)
Area of kite = 125 square meters.
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2. A ribbon is 5 long. A piece of length 3 4/5 is cut from it. What is the length of the remaining piece?
Answer:
Given,The ribbon is 5m long.
The length of the piece = 3 ^ 4 / 5 m.
To find,The length of the remaining piece.
Solution,We can simply solve this mathematical problem by using the following mathematical process.
First of all, we have to convert the length of the cut piece into simple decimal value.
Length of cut piece =3^ 4 / 5 = (3 * 5 + 4) / 5 = 19/5 = 3.8m
Length of the remaining ribbon = Intital length cut length = 5 - 3.8 = 1.2m = 12/10 - m = 6/5 * m = 1 1/5 m
(The final value is also expressed in fractional form)Hence, the length of the remaining piece is 15m.Answer: 1 1/5
Step-by-step explanation:
5 - 3 = 2 - 4/5 = 1 1/5
________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
What is DPU?Defects per unit (DPU) can be defined as the number of defects divided by the number of opportunities
It is also seen as the universal measure of quality.
For example, if there are 100 defects in 1,000 units produced, then the defects per unit will be 0.01.
Defects per million opportunities can be defined as a mathematical calculation of the estimated quality of a process
From this information, we can conclude that DPU and DPMO are measure of defects in a sample.
Thus, DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
Complete question is;
________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
a. DPMO, DPU
b. DPU, DPMO
c. RTY, FTY
d. FTY, RTY
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What are mathematical formulas placed in software that performs an analysis on a data set?
a. algorithm
b. intelligence
c. analytics fact
(A) Algorithms are mathematical formulas placed in software that performs an analysis on a data set.
What is an Algorithm?Algorithms are mathematical algorithms that are used in software to analyze data sets. An algorithm is a finite sequence of strict instructions used to solve a class of specialized problems or to execute a computation in mathematics and computer science. Algorithms serve as specifications for calculating and processing data. Algorithms can utilize artificial intelligence to perform automatic deductions and use mathematical and logical checks to reroute code execution down various paths. Alan Turing pioneered the use of human traits as metaphorical descriptors of machines with terminology like "memory," "search," and "stimulus."
Therefore, (A) algorithms are mathematical formulas placed in software that performs an analysis on a data set.
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The graph shows a system consisting of a linear equation and a quadratic equation.
What is the solution to the system?
need it kinda asap
The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown.
Quadratic and linear equationQuadratic equation are equation that has a leading degree of 2 while a linear equation has a leading degree of 1.
From the given graph, the curve shown has a two solutions which is the point where the curve intersect the x-axis.
For the graph shows a system consisting of a linear equation and a quadratic equation, the solution will be the points where the line intersects the parabola.
The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown
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Identify the inequality
that describes this graph.
y≤x + 5
y>x+5
The inequality that describes this graph is y ≥ x+5
How to determine the inequality?From the given graph, we have the following highlights:
The line of the graph is a closed lineThe upper part is shadedThe first highlight above implies, the inequality can be any of ≥ and ≤
While the second highlight above implies, the inequality is ≥
Hence, the inequality that describes this graph is y ≥ x+5
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Charlie began hiking from her campsite back to her car. Her campsite was located 9 miles from her car. She had walked for 1 hour and was 2 miles from her campsite when she realized she had forgotten her water bottle. She hurried back to her campsite in 0.5 hours, collected her water bottle, and rested for 0.5 hours. Then she began hiking back to her car at a quicker pace. She hiked for 3 more hours before she reached her car. Which graph represents Charlie's distance from her car at different times?
The graph which represents Charlies distance from her car at different times is indicated as attached. The schedule of her movement is also attached. This type of graph is called Distance Time Graph.
What is a distance-time graph?
A distance-time graph can show the distance traveled while an item moves in a straight line.
The gradient of the line in a distance-time graph is equal to the object's speed. The item is travelling more quickly the steeper the line and the larger the gradient.
See the attached for Charlies Distance - Time movements visualized in a graph.
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Near the equator, the earth rotates approximately 34 kilometers every 32 seconds. what is the speed of earth's rotation near the equator? show your reasoning and include the unit of measure.
Answer:
Step-by-step explanation: The earth rotates 34 km every 32 seconds. We can simplify this by dividing both sides by 32. Now, we have 34/32 km every 32 seconds. Now, to further simplify this, we need to convert 34/32 to a mixed number 34/32 = 1 2/32 which then can be simplified to 1 1/16. So, near the equator, the speed of Earth's rotation is 1 1/16 km per second.
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Cos C
C
21
B
35
28
A
Please help me if you can
The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:
Where w = weight of the car
p = power delivered by the engine in horsepower (hp)
If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.
Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer
Daniel’s answer was wrong because he used square root instead of the cubed root.
How can we calculate this?From the expression , which is [tex]t = 5.825 \sqrt[3]{3590/p}[/tex]
Then we can perform some operations to Solve for the value of p.
Then we can make division on the both sides of the equation using 5.825 , then we have
2.304 = [tex]} (3590/p)^{\frac{1}{3}[/tex]
We can cube the both side of the equation to will eliminate the radical and we will have
12.174 = 3590/p
then , p = 294.89 which implies that Natasha’s answer is correct.
Therefore , Daniel’s answer was wrong because he used square root instead of the cubed root.
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A vase in the shape of an oblique cylinder has the dimensions shown. What is the volume in the vase in liters?round nearest tenth
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Cylinder is solid geometrical figure with straight parallel sides and a circular or oval cross section
Let us assume that the vase has a base with radius of 1 m and height of 7 m, hence:
Volume of vase = π * radius² * height
Volume of vase = π * (1)² * 7 = 22 m³ = 22000 L
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
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The Data
Decorative glass pebbles are often used in vases for their appearance, and to have their weight stabilize the vase. The table below gives the total weight of a vase full of uniform glass pebbles.
TABLE OF DATA ATTACHED BELOW*
The Analysis
1- Using the table of data above, determine if this relationship is linear or not. Explain how you know.
2-Write an equation that best represents this relationship:
Explain how you reach your answer and show your work below.
3- Graph the data on the grid to the right, label both axes, and label it Line 1.
4-
a) What is the meaning of the initial value in this scenario?
b) What is the meaning of the slope in this scenario?
5- How would the graph AND equation change if a Styrofoam cup is used to collect the data, instead of a glass vase? Explain your reasoning.
6- Based on your equation in question #2, how much will 112 pebbles weigh with the vase?
7- If the total weight is 504 g, how many pebbles are in the vase?
8- Your friend Wilma shares her analysis of similar data about pebbles and a vase, but her equation is W = 10p + 80.
a) Graph it on the same grid as question #3. Label it Line 2.
b)What are the coordinates of the point of intersection?
c)What does it mean in this scenario?
9- Write a SIMPLIFIED algebraic expression to represent the area of the following trapezoid. Show all your work.
(Hint: area of a trapezoid = [tex]\frac{h(a+b)}{2}[/tex])
TRAPEZOID ATTACHED BELOW*
10- Tanya is 12 years older than Leah. Three years ago, Tanya was five times as old as Leah. What is the age of Tanya and Leah now?
I NEED IT TODAY PLESE!
With the aid of the attached diagrams in the question, we have;
1- Linear relation
2- W = 8•P + 80
3- Please find attached the graph created using a graphing calculator.
4- a) The initial value is the mass of the vase
b) The slope is the mass of each pebble
5- The initial value is lesser than 80
6- 1.2 kilograms
7- 53 pebbles
8- a)
b) (0, 80)
c) The masses are the same
9- Trapezoid area, A = 14•x² - 4•x
10- Tanya and Leah are 18 and 6 years old respectively
How can the table and diagram be analyzed?1- The relationship between two variables (x and y) is linear if the difference between the terms of the x-values and the terms of the y-values are both constant.
From the table we have;
The difference between consecutive terms of the x-values is constant and equal to 10The difference between consecutive terms of the y-values is constant and equal to 80The relationship between the x and y-values in the table is therefore;
A linear relationship2. The slope, m, of the linear function is found as follows;
m = (360 - 280)/(30 - 20) = 8
The equation is therefore;
W - 360 = 8•(P - 30)
W = 8•P - 240 + 360 = 8•P + 80
The equation is; W = 8•P + 803. Please find attached the graph drawn with a graphing calculator.
4. The initial value is the output variable (W-value) when the input variable (P-value) is zero.
Therefore;
y = 8×0 + 80 = 80
a) The initial value indicates when the input, P-value is zero, which gives the mass of the vases
b) The slope indicates the number of times an additional pebble increases the weight of the vase and pebble, which is the mass of one pebble
5- A styrofoam cup is lighter than a glass cup, therefore, the initial value, which is the constant term, c, reduces.
The change is that, the initial value reduces and becomes less than 806- The weight, W, of 112 pebbles is therefore;
W = 10 × 112 + 80 = 1,200
The weight of 112 pebbles is 1,200 g, which is 1.2 kg.7- 504 = 8•P + 80
Which gives;
504 - 80 = 8•P
P = 424 ÷ 8 = 53
The number of pebbles in the vase when it weighs 504 g. is 53 pebbles8- Wilma's equation is; W = 10•P + 80
a) Please find the second graph showing the graphs of the two equations combined.
b) The point of intersection is given by the relation 10•P + 80 = 8•P + 80
2•P = 0
P = 0
Therefore, at the point of intersection, W = 80
The coordinates of the point of intersection is therefore;
(0, 80)c) The point of intersection means that the weight of Wilma's vase and the vase in question 1 are the same.
9. The area of the trapezoid, A, can be expressed as follows;
A = 4•x × ((2•x + 5)+(5•x - 7))/2
A = 2•x × (7•x - 2) = 14•x² - 4•x
Area of the trapezoid = 14•x² - 4•x10. Let T represent Tanya's age now and let L represent Leah's current age, we have;
T = L + 12
T - 3 = (L - 3) × 5
Solving gives;
L + 12 - 3 = (L - 3) × 5 (Substitution property)
L + 9 = 5•L - 15
4•L = 9 + 15 = 24
L = 24 ÷ 4 = 6
Leah's age now, L = 6 yearsT = L + 12
Therefore;
T = 6 + 12 = 18
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Let a and b be 3 by 3 matrices with det (a) = 3 and det (b) = 5. find the value of det(ab).
If the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.
Given that the value of determinant a is 3, determinant b is 5.
We are required to find the value of determinant ab.
Determinant of a matrix is the scalar value computed for a given square matrix.It means the matrix which is not square does not have a determinant value. It is denoted by IAI.
We know that,
IaI*IbI=IabI
So we have to just put the values in the above formula to get the determinant of ab.
IabI=3*5
=15
Hence if the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.
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please please please please please please please please please please please please please please please please please help mey,
Answer:
See below
Step-by-step explanation:
REMEMBER sec = 1/cos ...so the left side is
[1/cos -1] / [1/cos +1 ]
get common denominator for numerator and denominator
[ (1 -cos) /cos ] / [ (1+cos) / cos ]
now flip the bottom fraction and multiply to get
[(1-cos/cos) ] * [ cos / (1+cos) ] which simplifies to ( the 'cos' term cancels)
(1-cos) / (1+cos) done !
A 7. 12×10−4mol sample of koh is dissolved in water to make up 50. 0ml of solution. what is the ph of the solution at 25. 0∘c? round the answer to three significant figures
The pH of the solution is 12.2.
Molarity (kon) = No. of moles of FoH x 1000
Mckor, 7:12 × 10-4 moles x Looo 50.0 mL.
Volume of solution (m²), McKong = 1.424x102M, [on] =1.424×102M POH = -log [on] pOH =
-log [1.424x102] pon = 1.85.
pH + pOH = 14
PH = 14-pOH = 14-1.85 pH = 12.15.)
12.2.
pH is a measure of the concentration of hydrogen ions in water. Specifically, pH is the negative logarithm of the hydrogen ion (H+) concentration (mol/L) in an aqueous solution. pH = -log10(H+) This term indicates the basicity or acidity of a solution from 0 to 14 where pH 7 is neutral.
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