Answers
Answer:
x =~ 31.2
y =~ 18
z =~ 9
Step-by-step explanation:
cos 30º = 27 / x
0.8660 = 27 / x
x = 27 / 0.8660
x =~ 31.18
w = height (smaller trinagle w, y, z)
tg 30º = w / 27
0.5774 = w / 27
w = 27 * 0.5774
w = 15.5898
tg 30º = z / 15.5898
0.5774 = z / 15.5898
z = 0.5774 * 15.5898
z = 9.00155052
cos 30º = 15.5898 / y
0.8660 = 15.5898 / y
y = 15.5898 / 0.8660
y =~ 18
Related Questions
I need help on this!
Answers
Answer:
He is now selling only one product and making less money because he is not selling other TVs.
Step-by-step explanation:
So if you read the paragraph, you get to the point where he says only making and selling the television model that makes the most money. If you think about it if they only sell one product, the other products they used to sell aren't being sold and they are making less money. I hope this helps!
please show work!!!!!!!
Answers
Answer:
J. 56
Step-by-step explanation:
The picture in this question can be a little deceiving. Each rectangular glass pane is 3 by 10 inches. This means that the picture of the 4 panes overlapping, leaves the center square open. The open area has your inner edges. The question asks for the sum of the inner and outer edges.
Every pane is 10 inches long, so the out perimeter of the figure is 40 inches because the figure has four sides. The rectangles overlap, creating 3 by 3 inch square. 3 inches off either side of a pane leaves 4 inches as the length for the edge of the inner square. Therefore, the perimeter of the inner square is 16 inches.
Outer Perimeter + Inner Perimeter = 40 + 16 = 56 inches
Please refer to the photo!
Answers
A population has a standard deviation of sigma = 24. a. On average, how much difference should exist between the population mean and the sample mean for n = 4 scores randomly selected from the population? b. On average, how much difference should exist for a sample of n = 9 scores? c. On average, how much difference should exist for a sample of n = 16 scores?
Answers
Therefore , the solution of the given problem of standard deviation comes out to be he average difference between the population mean and the sample mean is 6.
What is standard deviation?Variance is a measure of variation used in statistics. The average difference between the gathering and the mean is calculated using the photo of that figure. By comparing each number to the mean, it incorporates those data points into the calculations on their own, in contrast to many other legitimate measures of variable. Variations could result from deliberate errors, unrealistic expectations, or changing economic or commercial circumstances.
Here,
For a group of n = 4, the standard error of the mean (SEM) is as follows:
=> SEM = α/√(n)
=> 24/√(4) = 12
Therefore, for n = 4 scores drawn at random from the population, the average difference between the population mean and the sample mean is 12.
b. The SEM for a group of n = 9 is:
=> α/√(n) = 24/√(9)
=> 8; SEM = α
Therefore, for n = 9 scores drawn at random from the population, the average difference between the population mean and the sample mean is 8.
c. The SEM for a sample of 16 is as follows:
=> α / √(n) = 24 / √(16) = 6;
=> SEM =α
Therefore, for n = 16 scores drawn at random from the population, the average difference between the population mean and the sample mean is 6.
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The intensity of sound from the stands of a football game is 30 times as great when the home team scores a touchdown as it is when the away team scores. Find the difference in the loudness of the sound when the two teams score. Round your answer to the nearest hundredth.
The difference in the loudness of sound is about _______ decibels
Answers
The difference in the loudness of sound when the two teams score is about 14.77 decibels
What is sound intensity ?Sound intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.
We can use the fact that the loudness of sound is measured in decibels (dB) and that the dB scale is logarithmic.
Let's assume that the loudness of the sound when the away team scores is x decibels. Then the loudness of the sound when the home team scores a touchdown is 30 times as great, which means it is 30x decibels.
The difference in loudness between the two scenarios is given by the difference in decibels:
difference in decibels = 10 log (30x/x) = 10 log 30 = 14.77
Therefore, the difference in the loudness of sound when the two teams score is about 14.77 decibels
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Cumulative distribution function for a continuous random variable x
Answers
The cumulative distribution function gives us the probability that the random variable is less than or equal to a given value.
The cumulative distribution function (CDF) of a continuous random variable x is a function which gives the probability that the random variable x is less than or equal to a given value x. Mathematically it is expressed as:
[tex]F(x) = P(X ≤ x)[/tex]
The calculation of the cumulative distribution function is done by integrating the probability density function (PDF) from the lower limit to the given value x. Thus,
[tex]F(x) = ∫-∞ x f(u) du[/tex]
Where f(u) is the probability density function.
For example, if we have a continuous random variable x with probability density function f(x) = x2, then the cumulative distribution function [tex]F(x) = ∫-∞ x x2 du = 1/3x3 + c.[/tex]
Thus, It is a powerful tool for analysing the probability distribution of a continuous random variable.
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Complete question:
What is the cumulative distribution function for a continuous random variable x?
The diameter of a circle is 17 ft. Find its area to the nearest whole number.
Answers
Answer:
[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the area of a circle.}[/tex]
[tex]\textsf{First, we should identify the formula for the area of a circle.}[/tex]
[tex]\large\underline{\textsf{Formula:}}[/tex]
[tex]\mathtt{Area = \pi (radius)^{2}}[/tex]
[tex]\textsf{The radius is \underline{half} of the diameter.}[/tex]
[tex]\mathtt{\frac{17}{2} = 8.5ft.}[/tex]
[tex]\textsf{Let's begin solving for the area.}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{Area = \pi (8.5)^{2}}[/tex]
[tex]\mathtt{Area = 72.25 \pi}[/tex]
[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]
A catapult launches a pumpkin from the base of a hill. The hill follows an incline with the
height in meters, y, in terms of horizontal distance in meters, x, given by the equation
y=0. 9x. The height of the pumpkin, as it is launched uphill, is given by the function
y = -0. 1x² +4. 9x
What is the height, in meters, where the pumpkin lands on the hill?
Answers
The height, in meters, where the pumpkin lands on the hill is 4.9 meters.The equation for the height of the hill is y = 0.9x.
This equation can be rearranged to solve for x, giving x = y/0.9. The equation for the height of the pumpkin is y = -0.1x² + 4.9x. Substituting the x value from the previous equation into the equation for the height of the pumpkin gives y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying this equation gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill.
The equation for the height of the hill is y = 0.9x, which describes the incline of the hill. This equation can be rearranged to solve for x, giving x = y/0.9. This equation can then be used to substitute into the equation for the height of the pumpkin, which is y = -0.1x² + 4.9x. When the x value from the previous equation is substituted into the equation for the height of the pumpkin, the equation simplifies to y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying further gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill. This can be verified by substituting 4.9 for y in the equation for the height of the hill, which gives x = 4.9/0.9 = 5.4. This value can be substituted into the equation for the height of the pumpkin, which gives y = -0.1(5.4)² + 4.9(5.4) = 4.9, verifying the result.
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what is the result of substituting for y in the bottom equation?
Answer:
A. y=(x-3)^2+2(x-3)-4
B. x-3=x^2+2x-4
C. y=x^2+2x-4-(x-3)
D. (x-3)=x^2
Answers
Optiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 =x² + 2x - 4.
What is the equivalent expression?Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.
Tο substitute fοr y in the secοnd equatiοn, we can replace y with its equivalent expressiοn in terms οf x frοm the first equatiοn, which gives us:
x - 3 = x² + 2x - 4
This is option B.
Optiοn A is incοrrect because it substitutes y fοr its expressiοn in terms οf x in the wrοng equatiοn.
Optiοn C is incοrrect because it subtracts (x-3) instead οf adding it tο the secοnd equatiοn.
Optiοn D is incοrrect because it sets the expressiοn fοr y in the first equatiοn equal tο x² instead οf the expressiοn fοr y in the secοnd equatiοn.
Hence, οptiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 = x² + 2x - 4.
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Complete question:
What is result of substituting for y in the bottom equation?
y = x – 3,
y = x² + 2x – 4
A. y=(x-3)²+2(x-3)-4
B. x-3=x²+2x-4
C. y=x²+2x-4-(x-3)
D. (x-3)=x²
An iPhone costs £800 in London, €880 in Paris and $850 in New York. Using £1 = €1.16 and £1 = $1.41, state the lowest price of the iPhone in £. Give your answer to 2 dp.
Answers
Answer:
£602.84 in New York
Step-by-step explanation:
London Cost:
Converting pound to dollars:
£800 * 1.41 = $1128
Paris cost:
Converting euro to pounds:
€880/1.16 = £759
Converting pound to dollars again:
£759 * 1.41 = $1070
New york cost:
$850
The lowest price is in new york which is:
$850/1.41 = £602.84
Feel free to mark this as brainliest (I'm one brainliest off 50 so please help out
The 1989 U. S. Open golf tournament was played on the East Course of the Oak Hills Country Club in Rochester, New York. During the second round, four golfers scored a hole in one on the par 3 sixth hole. The odds of a professional golfer making a hole in one are estimated to be 3,708 to 1, so the probability is 1/3,709. There were 175 golfers participating in the second round that day. A. What is the probability that no one gets a hole in one on the sixth hole
Answers
The probability that no one gets a hole on the sixth hole is given as follows:
0.9534 = 95.34%.
What is the binomial distribution formula?The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The mass probability formula is given as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 175 -> number of golfers.p = 1/3709.The holes are independent, hence the probability of no one getting a hole in the sixth hole is P(X = 0), thus:
P(X = 0) = (1 - 1/3709)^175
P(X = 0) = 0.9534 = 95.34%.
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what is value expression
1.3(X + 2)-(y - 6)
when X= 4 and Y= 2
a 1.1
b 11.8
c 2.6
d 26
Answers
The value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2 is Option B: 11.8.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
To find the value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2, we substitute these values into the expression and simplify -
Substitute the values x = 4 and y = 2 into the expression -
1.3(x + 2) - (y - 6)
= 1.3(4 + 2) - (2 - 6)
Apply the addition and subtraction operation -
= 1.3(6) - (-4)
Apply the multiplication operation -
= 7.8 + 4
= 11.8
Therefore, the value of the expression is 11.8.
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A triangular prism with dimensions 8 inches by 13 inches
by 16 inches in placed in a box of the same dimensions, as
show in the figure below. How many cubic inches of filler
material are required to surround the triangular prism in
order to completely fill the box?
=.
.
104
416
832
1,664
13
Cannot be determined by the given information
8
16
Answers
To fully describe a triangular prism, you would need to provide the dimensions of its triangular bases (e.g. base length and height), the length of the prism, and the length and width of the rectangular faces. Thus, option C is correct.
What is the triangular prism with dimensions?To find the volume of filler material required to surround the triangular prism, we need to first calculate the volume of the box and the volume of the triangular prism.
The volume of the box is given by:
[tex]8[/tex] inches × [tex]13[/tex] inches × [tex]16[/tex] inches = [tex]1,664[/tex] cubic inches
The volume of the triangular prism is given by:
[tex](1/2) × 8[/tex] inches × [tex]13[/tex] inches × [tex]16[/tex] inches = [tex]832[/tex] cubic inches
To completely fill the box, we need to add filler material with a volume equal to the difference between the volume of the box and the volume of the triangular prism, which is:
cubic inches— [tex]832[/tex] cubic inches [tex]= 832[/tex] cubic inches
Therefore, the [tex]832[/tex] Cubic inches.
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Please ASAP Help
Will mark brainlest due at 12:00
Answers
Answer:
plot the point at 1
Step-by-step explanation:
A grocer has two kinds of candy, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
Answers
Answer:The quantity of grocer of price $1.40 is 45 pounds
The quantity of grocer of price 40 cents is 55 pounds
Step-by-step explanation:
Let The quantity of one grocer = x pound
Let The quantity of other grocer = y pound
The selling price of x grocer = 40 cents per pound
The selling price of y grocer = $ 1.40 per pound = 1.40 × 100 = 140 cents
Total quantity = 100 pounds
Total price of both grocer = 85 cents
According to question
x + y = 100 .........A
And
40 × x + 140 y = 85 × 100
Or, 40 x + 140 y = 8500 ........B
Solving eq A and eq b
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
Or, (40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
or, 0 + 100 y = 4500
∴ y =
i.e y = 45 pounds
So, The quantity of grocer of price $1.40 = y = 45 pounds
Again
Put the vaue of y in eq A
x + y = 100
i.e x = 100 - y
or, x = 100 - 45
∴ x = 55 pounds
So, The quantity of grocer of price 40 cents = x = 55 pounds
Hence, The quantity of grocer of price $1.40 is 45 pounds
And The quantity of grocer of price 40 cents is 55 pounds Answer
Therefore, the grocer must use 55 pounds of the 40-cent candy and 45 pounds of the $1.40 candy to make 100 pounds worth 85 cents a pound
Step by step explanation:
Let x be the number of pounds of the 40-cent candy and y be the number of pounds of the $1.40 candy.
We can set up a system of equations based on the information given:
x + y = 100 (1) (the total amount is 100 pounds)
0.4x + 1.4y = 0.85(100) (2) (the cost of 100 pounds is $85)
Simplifying equation (2), we get:
0.4x + 1.4y = 85
Multiplying both sides by 10, we get:
4x + 14y = 850 (3)
Now, we can use equations (1) and (3) to solve for x and y. We can solve equation (1) for x:
x = 100 - y
Substituting this expression for x into equation (3), we get:
4(100 - y) + 14y = 850
Expanding and simplifying, we get:
400 - 4y + 14y = 850
10y = 450
y = 45
Substituting y = 45 into equation (1), we get:
x + 45 = 100
x = 55
Therefore, the grocer must use 55 pounds of the 40-cent candy and 45 pounds of the $1.40 candy to make 100 pounds worth 85 cents a pound.
A bakery sells apple pies for $12.85. if the pie has a diameter of 10 inches, what is the approximate cost per square inch of the apple pie? round to the nearest hundredth. a. $0.04 b. $0.16 c. $0.32 d. $0.65
Answers
The cost per square inch of the apple pie is $ 0.16.
Given that,
The diameter of the pie = 10 in
The radius of the pie = 10/2
= 5 inches.
Area of the pie = [tex]\pi r^{2}[/tex]
= 3.14 × 5²
= 3.14 × 25
= 78.5 in²
The cost of the apple pie = $ 12.85.
Therefore, the cost per square inch of the pie = 12.85 ÷ 78.5
= $ 0.16.
Hence, the cost per square inch of the apple pie is $ 0.16.
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A cylindrical soup can is 6 cm in diameter and 12 cm tall.
A. If the diameter is 6 cm, what is the radius?
B. We use the formula to find the surface area of a cylinder (with r = radius & h = height).
C. Plug your "r", "h", and " 3.14 for n" into the formula.
Show your work and label your final answer to find the surface area of the soup can.
Please only help me if your going to help
Answers
Answer:
A. If the diameter is 6 cm, then the radius is half of that:
radius = 6 cm / 2 = 3 cm
B. The formula for the surface area of a cylinder is:
S.A. = 2πr^2 + 2πrh
C. Plugging in the values for r, h, and π:
S.A. = 2π(3 cm)^2 + 2π(3 cm)(12 cm)
S.A. = 2π(9 cm^2) + 2π(36 cm^2)
S.A. = 18π cm^2 + 72π cm^2
S.A. = 90π cm^2
Therefore, the surface area of the soup can is 90π square centimeters. This can be simplified to approximately 282.74 square centimeters by using the value 3.14 for π.
Please help me! A sector has a central angle measure of 90 degrees, and a radius of 8 cm. Which equation shows the correct calculation of the area of the sector?
Answers
Therefore , the solution of the given problem of area comes out to be
A = 16 is the equation that accurately depicts how to calculate the sector's area.
What is an area ?Its total size can be determined by figuring out how much space is required to completely cover the outside. The immediate surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. A cuboid's capacity for internal water is determined by the sum of the borders that link all of it's six rectangle edges.
Here,
The formula for calculating a circle's sector's area is:
=> A = (θ/360) x πr²
where A is the sector's area, is its central angle measurement, and r is the circle's radius.
Since the radius is 8 cm and the central angle is 90 degrees in this instance, we can reduce by plugging in these values:
=> A = (90/360) x π(8²)
=> A = (1/4) x π(64)
=> A = π(16)
=> A = 16π
A = 16 is the equation that accurately depicts how to calculate the sector's area.
The answer will be given in radius squared units, in this case, cm2.
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Option D. The correct calculation of the area of the sector is [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]
What is an area of the sector?An area of the sector is the portion of the area of a circle that is enclosed by two radii and an arc. The area of a sector can be found using the formula:
A = (θ/360)πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Given, the radius is 8 cm and the central angle is 90° in this instance, put all these values:
[tex]A=(\frac{90}{360}) * \pi (8^{2} )[/tex]
or we can write down, [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]
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The radius of circle B
is 4 centimeters and the circumference of
Circle A is 30 pi
centimeters. Find CD.
Answers
Find CD:
Let,
[tex]r_1[/tex] be a radius of Circle A
[tex]r_2[/tex] be a radius of Circle B
Given:
[tex]r=4cm.[/tex]
Circumference: [tex]2\pi r[/tex]
[tex]2\pi r_1=30[/tex]
[tex]r_1=\dfrac{15}{\pi }[/tex]
[tex]CD=D_1+D_2[/tex]
[tex]=2r_1+2rx_2[/tex]
[tex]=2\times(\dfrac{15}{\pi })+2\times4[/tex]
[tex]CD=17.55cm.[/tex]
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Question 1: The perimeter of the triangle below is 5x^3 - 2x^2 + 3x - 8.
Part A: Given the information below. What is the total length of sides 1 and 2 of the triangle? SHOW ALL WORK! (MANDATORY)
Side 1: 3x^2 - 4x - 1
Side 2: -x^2 + 4x + 5
Answer: Side 1 + Side 2 = _______ (MANDATORY)
Part B: What is the length of the 3rd side of the triangle? Show your work.
5x^3 - 2x^2 + 3x - 8 - (________) =
Answer (Drag & Drop):
A) 5x^3 - 4x^2 + 3x - 4
B) 5x^3 - 4x^2 + 3x - 12
C) 5x^3 - 4x^2 + 3x + 12
D) 5x^3 - 4x^2 + 3x + 4
Answers
Answer:
Part A:
To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:
Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)
Simplifying the expression by combining like terms, we get:
Side 1 + Side 2 = 2x^2 + 1
Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.
Part B:
To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:
5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]
Simplifying the expression by distributing the negative sign, and then combining like terms, we get:
5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4
Simplifying further by combining like terms, we get:
5x^3 - 4x^2 + 11x - 4
Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.
Answer:
A) 5x^3 - 4x^2 + 3x - 4
Step-by-step explanation:
Answer:
A) 5x^3 - 4x^2 + 3x - 4
Step-by-step explanation:
Part A:
To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:
Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)
Simplifying the expression by combining like terms, we get:
Side 1 + Side 2 = 2x^2 + 1
Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.
Part B:
To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:
5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]
Simplifying the expression by distributing the negative sign, and then combining like terms, we get:
5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4
Simplifying further by combining like terms, we get:
5x^3 - 4x^2 + 11x - 4
Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.
Answer:
A) 5x^3 - 4x^2 + 3x - 4
How long is the base of a parallelogram if it has an area of 60 square feet and a height of 10 feet? 6 feet 50 feet 60 feet
Answers
Answer:6 feet
Step-by-step explanation:
The formula for the area of a parallelogram is:
Area = base x height
We know that the area is 60 square feet and the height is 10 feet, so we can plug these values into the formula and solve for the base:
60 square feet = base x 10 feet
Dividing both sides by 10 feet gives:
6 feet = base
HELP PLEASE ASAP!!!!
Triangle PQR with coordinates P(-3,4). Q(-6,1), and R(-6,6) is reflected over the x-axis. List the coordinates of the new image
Answers
Answer:
P(0,2), Q(3,5), R(3,0)
Step-by-step explanation:
An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $4500 and her stock in Company B was worth $3900. The stock in Company A has increased 5% since last year and the stock in Company B has increased 11%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
Answers
The total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.
To calculate the total percentage increase in the investor's stock account, we first need to calculate the new values of the stocks in Company A and Company B after the increase.
The new value of the stock in Company A is:
[tex]4500 + (5 \times 4500) = $4725[/tex]
The new value of the stock in Company B is:
[tex]3900 + (11 \times 3900) = 4339[/tex]
The total value of the investor's stock account after the increase is:
$4725 + $4339 = $9064
To calculate the percentage increase in the investor's stock account, we need to find the difference between the new total value and the original total value, and then divide that difference by the original total value:
($9064 - $8400) / $8400 = 0.0795
We then multiply this decimal by 100 to get the percentage increase:
0.0795 x 100 = 7.95%
Therefore, the total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).
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Mr Keag's swimming pool is 15 feet long, 12 feet wide and 10 feet deep. How much water would it take to fill it half way to the top
Answers
Answer:
900 cubic feet
Step-by-step explanation:
[tex] \frac{1}{2} (15 \times 12 \times 10) = \frac{1}{2} (1800) = 900[/tex]
A. What is the magnitude of an earthquake with amplitude 100,000? How
do you know?
Answers
The magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale
What do you mean by Magnitude and amplitude in term of Earthquake ?Magnitude: The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. It is typically determined using a logarithmic scale called the Richter scale or other similar scales like the moment magnitude scale (MMS), surface wave magnitude (Ms), or body wave magnitude (Mb). The Richter scale is based on the amplitude of the largest seismic wave recorded on a seismographs, and each increase of one unit on the scale corresponds to a ten-fold increase in the amplitude of the seismic waves and a 32-fold increase in the amount of energy released.
Amplitude: The amplitude of an earthquake is the size of the seismic waves that are generated by the earthquake. It is measured in microns (millionths of a meter) and is recorded on a seismographs. The amplitude of seismic waves can vary greatly depending on the distance from the earthquake's epicenter and the geological structure of the surrounding area.
The magnitude of an earthquake is a measure of the amount of energy released during the earthquake, and is typically determined using a logarithmic scale called the Richter scale.
The formula for calculating the magnitude of an earthquake based on its amplitude is:
Magnitude = log10 (Amplitude) - 3
where the amplitude is measured in microns.
Assuming the amplitude of the earthquake is 100,000 microns, we can calculate its magnitude as:
Magnitude = log10 (100,000) - 3
Magnitude = 5 - 3
Magnitude = 2
Therefore, the magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale.
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The mass of a sheet of metal varies jointly with it's area and it's thickness. A sheet of metal of area 250cm and thickness 1mm has a mass of 200g
Answers
The mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.
The mass of a sheet of metal is directly related to its area and thickness. This means that the mass of a sheet of metal is proportional to the product of its area and its thickness. Mathematically, this can be expressed as the formula M = kAT, where M is the mass, k is a constant, A is the area and T is the thickness.In the given example of a sheet of metal with an area of 250 cm and a thickness of 1mm, we can calculate the mass of the sheet by substituting the given values into the formula: M = k(250)(1) = 200g. The constant k in this example is equal to 0.8 g/cm*mm.Therefore, the mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.
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What is the mass of a sheet of metal with an area of 250cm and a thickness of 1mm?
The graph shows a two-dimensional side view of a
satellite dish and the small reflector inside it. The vertex
of the small reflector is 6 in. from focus F₁ and 20 in. from
focus F2. What equation best models the small reflector?
Picture of graph attached !!! please help
Answers
The equation is -7x+y=0.
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, The equation is -7x+y=0.
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Mr. Sharma has the option of selecting a rectangular plot of size 45 m × 25 m or a square plot of
size 35 m at the same price. Which one should he prefer and why?
Answers
Answer:
Square Plot
Step-by-step explanation:
Let us compare the Area of both plots
Rectangular Plot : L X B = 45 x 25 = 1125 M^2
Square Plot : S X S = 35 x 35 = 1225 M^2
Area of Square Plot > Area of Rectangular Plot
Therefore he should prefer the Square Plot as it has more area.
Hope it helps.
A screen door spring has a spring constant of 188 N/m, and stretches 0. 292 m when the door is opened. What force does it exert?
(Unit = N)
Answers
If the screen door spring has a spring constant of 188 N/m, then the force it exert is 54.9 N .
The force exerted by the screen door spring can be calculated using Hooke's law,
The Hooke's Law states that the force exerted by a spring is directly proportional to its spring constant and the amount it is stretched.
The formula for "Hooke's-law" is ⇒ F = kx
Where F is = force exerted by spring, k is = spring constant, and x is = amount spring is stretched.
In this case , the spring constant(k) = 188 , the distance stretched(x) = 292m ;
Substituting the values,
We get,
⇒ F = (188 N/m)(0.292 m)
⇒ F = 54.896 N
⇒ F ≈ 54.9N
Therefore, The force exerted by the screen door spring is approximately 54.9 N.
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write an equation in slope-intercept form of the line that passes through the given points
[tex]\left[\begin{array}{ccc}x&y\\-4&9\\-2&4\\0&-1\\2&-6\end{array}\right][/tex]
Answers
Answer:
y = - [tex]\frac{5}{2}[/tex] x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 9) and (x₂, y₂ ) = (2, - 6) ← 2 ordered pairs from the table
m = [tex]\frac{-6-9}{2-(-4)}[/tex] = [tex]\frac{-15}{2+4}[/tex] = [tex]\frac{-15}{6}[/tex] = - [tex]\frac{5}{2}[/tex]
the line crosses the y- axis at point (0, - 1 ), ordered pair from table, then
c = - 1
y = - [tex]\frac{5}{2}[/tex] x - 1 ← equation of line