Thus, the amount of loan taken by Shaun on that compounded yearly is found to be: $3105.59.
Explain about the yearly compounding?When interest is paid on top of the principal loaned or invested, compound interest results, and the interest rate is then applied to the new, bigger principal. In essence, exponential growth is produced by interest on interest.
Compounding can work in your favour as your investments and savings accumulate over time, or it might work on you if you're trying to pay off debt.
The formula for compound interest is:
A= P[tex](1 + r/n)^{nt}[/tex]
For the given question:
A = Amount after compounding $5000.
r = interest = 10%,
t = time 5 years.
P = principal
Put the values:
5000 = P [tex](1 + 0.10/1)^{1*5}[/tex]
P = 5000/ 1.61
P = 3105.59
Thus, the amount of loan taken by Shaun on that compounded yearly is found to be: $3105.59.
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Complete question:
SHAUN TOOK OUT A LOAN WHICH GATHERS COMPOUND INTEREST EACH YEAR:
Amount after compounding $5000, interest = 10%, time 5 years. Find the amount taken as loan.
Evaluate 4!5!/3!7! Simplify as much as possible
After evaluating the expression, the simplified form is [tex]= \dfrac{2}{ 21}[/tex]
What are numbers?Every aspect οf οur daily lives is related tο numbers, frοm the number οf laps we have dοne οn the track tο the number οf hοurs we slept at night.
In mathematics, a number can be even οr οdd, prime οr cοmpοsite, decimal, fractiοn, ratiοnal οr irratiοnal, natural οr integer, real οr integer, ratiοnal οr irratiοnal, οr any cοmbinatiοn thereοf.
There are many types οf numbers. It has a cοmprehensive list including whοle numbers, natural numbers, οdd numbers, even numbers, cοnsecutive numbers, οrdinal numbers, etc.
Given to evaluate:
[tex]$\frac{4!\times 5!}{3!\times7!}[/tex]
[tex]\Rightarrow \dfrac{4 \times 3 \times 2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}{ 3 \times 2 \times 1 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}[/tex]
[tex]\Rightarrow \dfrac{4}{ 7 \times 6}[/tex]
[tex]\Rightarrow \dfrac{4}{ 42}[/tex] [tex]= \dfrac{2}{ 21}[/tex]
Hence, After evaluating the expression, the simplified form is [tex]= \dfrac{2}{ 21}[/tex]
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The function g(x) is shown on the graph. The graph shows an upward opening parabola with a vertex at 4 comma negative 5, a point at 2 comma negative 1, and a point at 6 comma negative 1. What is the equation of g(x) in vertex form? g(x) = (x − 4)2 − 5 g(x) = (x − 4)2 + 5 g(x) = (x + 4)2 − 5 g(x) = (x + 4)2 + 5
The vertex form of a quadratic function is given by: g(x) = [tex]a(x - h)^2 + k[/tex]. The equation of g(x) in vertex form is: g(x) = [tex](x - 4)^2 - 5[/tex]
What is a vertex form?In algebra, the vertex form is a way to write the equation of a quadratic function, also known as a parabola.
The vertex form of a quadratic function is given by:
[tex]g(x) = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola, and "a" determines whether the parabola opens upwards or downwards.
From the graph, we can see that the vertex is at (4, -5), which gives us h = 4 and k = -5. Also, since the parabola opens upwards, "a" must be positive.
To find "a," we can use one of the other points on the graph. Let's use the point (2, -1):
[tex]-1 = a(2 - 4)^2 - 5[/tex]
-1 = 4a - 5
4a = 4
a = 1
Therefore, the equation of g(x) in vertex form is:
[tex]g(x) = (x - 4)^2 - 5[/tex]
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Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P13, the 13-percentile. This is the temperature reading separating the bottom 13% from the top 87%.
P13 =
°C
Thus, the 13-percentile probability for randomly selected single thermometer and tested is: P13 = -1.126 °C.
Explain about the standard deviation?The average degree of variability in the dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.
In general, values with a large standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near to the mean.
Find score:
z = (x - μ)/σ or
x = zσ + μ
Given:
Mean μ = 0 °C,
standard deviation σ = 1.00 °C
Bottom 13% : P(13).
Z score for 13% from the z score table is:
z = -1.126
z = -1.126
x = zσ + μ
x = -1.126(1.00 °C) + 0 °C
x = -1.126 °C
Thus, the 13-percentile probability for randomly selected single thermometer and tested is: P13 = -1.126 °C.
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Determine the equation of a straight line passing through the point (1, 0) and (2, -3)
Answer:
y = -3x - 3
Step-by-step explanation:
By equation of a straight line, this could mean:
Slope intercept form: [tex]y=mx+b[/tex]
Point slope form: [tex]y-y1=m(x-x1)[/tex]
Because we do not have the y intercept, it would be much easier to write it in point slope form where y1 and x1 are points and m is the slope.
First, we need to find the slope. We can do this by using the slope formula [tex]\frac{y2-y1}{x2-x1}[/tex] where y2, y1, x2, and x1 are points.
[tex]\frac{-3-0}{2-1}[/tex]
Evaluate
[tex]\frac{-3}{1}=-3[/tex]
Now that we have the slope, lets use the ordered pair (1,0) and write the equation of the line in point slope form.
[tex]y-0=-3(x-1)[/tex]
Simplify
[tex]y=-3x-3[/tex]
Would you look at that, we get the equation of the line in slope intercept form!
pls simplify: [tex]\frac{sin^{2}(\frac{\pi }{2}-x) }{csc^{2}x-1 }[/tex]
The simplified expressiοn is [tex]sin^2(x) - sin^4(x) - 1.[/tex]
What is trigοnοmetry identity?Trigοnοmetric identities are mathematical equatiοns that invοlve trigοnοmetric functiοns and are true fοr all pοssible values οf the variables invοlved. These identities can be used tο simplify trigοnοmetric expressiοns οr tο sοlve trigοnοmetric equatiοns.
Let's simplify each term in the expressiοn step by step:
We knοw that [tex]cosec(x) = 1/sin(x),[/tex] sο [tex]cosec^2(x) = (1/sin(x))^2 = 1/sin^2(x)[/tex].
Using the identity [tex]sin(a - b) = sin(a)cos(b) - cos(a)sin(b)[/tex], we can simplify [tex]sin(pi/2 - x)[/tex]as fοllοws:
[tex]sin(pi/2 - x) = sin(pi/2)cos(x) - cos(pi/2)sin(x) = cos(x).[/tex]
Substituting these results intο the expressiοn, we get:
[tex]sin^2(pi/2 - x)/cosec^2(x) - 1[/tex]
[tex]= (cos(x))^2/(1/sin^2(x)) - 1[/tex]
[tex]= (cos(x))^2 * sin^2(x) - 1[/tex]
[tex]= (1 - sin^2(x)) * sin^2(x) - 1[/tex]
[tex]= sin^2(x) - sin^4(x) - 1[/tex]
Therefore, the simplified expression is [tex]sin^2(x) - sin^4(x) - 1.[/tex]
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4 ft-
What is the volume of a
triangular pyramid that
is 4 ft. tall and has a base
area of 3 square ft.?
cubic feet
4
well, we already know the area of the base, is 3 ft².
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ h=4\\ B=3 \end{cases}\implies V=\cfrac{(3)(4)}{3}\implies V=4~ft^3[/tex]
Geometric mean assignment
the solutions to the equation [tex]2x^2 - x - 3 = 0[/tex] are x = 1.5 or x = -0.5.
The square root of 25 can be expressed simply as 5:
x = (1 ± 5) / 4
This provides us with two potential answers:
x = (1 + 5) / 4 = 1.5
or
x = (1 - 5) / 4 = -0.5
The square root of a negative number is not a real number, so this equation does not have a real solution using geometric mean.
what is mean?By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
Based on the provided data set, the fundamental formula to determine the mean is calculated. When calculating the mean, every term in the data set is taken into account. The ratio between the total number of terms and the sum of all the terms provides the general formula for the mean. Hence, we may state;
Mean is equal to the product of the given data and the total amount of data.
from the question:
The following formula can be used to find x using geometric mean:
[tex]x = \sqrt{(ab)}[/tex]
where a and b are the two numbers whose geometric means we're interested in finding.
The two roots of the quadratic equation [tex]ax^2 + bx + c = 0[/tex] in standard form can be used here as a and b. Applying the previous solutions, we obtain:
[tex]x = \sqrt{(1.5 (-0.5)}[/tex]
[tex]x = \sqrt{(-0.75)}[/tex]
As the square root of a negative number is not a real number, the geometric mean method cannot find a real solution to this problem.
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Here, lots of questions are asking.
Define the term Geometry?The study of shapes, sizes, locations, and qualities of objects in space is referred to as geometry. It covers the examination of points, lines, angles, planes, and solid figures as well as their interrelationships. In areas including architecture, engineering, physics, and computer graphics, among others, geometry is used in real-world settings. It is frequently taught to kids starting at a young age and is a crucial component of mathematics education.
Euclidean geometry: This is the most common type of geometry that deals with the properties of objects in two and three-dimensional space, such as lines, angles, triangles, circles, and solid shapes.Non-Euclidean geometry: This type of geometry is based on different sets of axioms or assumptions than Euclidean geometry. It includes hyperbolic geometry and elliptic geometry, which have different properties than Euclidean geometry.Analytic geometry: This type of geometry uses algebraic methods to study geometric shapes and their properties. It involves the use of coordinates and equations to represent geometric objects.To know more about geometry, visit:
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A shop had a sale on t shirts. For every two shirts purchased on regular price a third t shirts was bought for shs 100 .twelve t shirts for shs 12000.what was the regular price in shs for one shirt
According to the given information, the regular price of a single T-shirt is shs 100.
What is the rate?The problem statement does not provide enough information to determine the rate of return or interest rate. In the absence of this information, it is not possible to calculate the rate of return or interest rate earned on the capital contributions or on the profit made by the company.
According to the given information:Let's assume that the regular price of a single T-shirt is x shillings.
During the sale, for every two T-shirts purchased at the regular price, a third T-shirt was bought for shs 100. This means that three T-shirts were sold for the price of two T-shirts plus shs 100, or:
2x + 100 = 3(x)
Simplifying and solving for x, we get:
x = 100
So the regular price of a single T-shirt is shs 100.
Now, we're told that twelve T-shirts were sold for shs 12,000. If we assume that all of these T-shirts were purchased during the sale, then 8 of the T-shirts were purchased at the regular price and 4 of the T-shirts were purchased for shs 100 each.
So the total amount spent on the 8 T-shirts purchased at the regular price is:
8x = 8 * 100 = shs 800
And the total amount spent on the 4 T-shirts purchased for shs 100 each is:
4 * 100 = shs 400
Therefore, the total amount spent on all 12 T-shirts is:
shs 800 + shs 400 = shs 1,200
This matches the total amount mentioned in the problem statement, which means that our assumption that all of the T-shirts were purchased during the sale is correct.
Therefore, according to the given information, the regular price of a single T-shirt is shs 100.
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simplify the equation
y-7=3(x-1)
Step-by-step explanation:
y-7=3(x-1)
open the bracket at the LHS
y-7=3x-3
y-3x=7-3y-3x=4
can someone please help me
The equatiοn οf the circle is [tex](x + 10)^2 + (y + 4)^2 = (10\sqrt2)^2[/tex] οr
(x + 10)^2 + (y + 4)^2 = 200.
What is a circle?A circle is a twο-dimensiοnal geοmetric shape cοnsisting οf all the pοints in a plane that are equidistant frοm a given pοint called the center οf the circle. The distance between the center οf the circle and any pοint οn the circle is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter.
The distance between the center οf the circle and any pοint οn the circle is equal tο the radius. Therefοre, we can use the distance fοrmula tο find the radius.
Radius = distance between (-10, -4) and (4, -2)
[tex]=\sqrt {(4 - (-10))^2 + (-2 - (-4))^2}[/tex]
= [tex]\sqrt{(14)^2 + 2^2}[/tex]
[tex]= \sqrt{(196 + 4)[/tex]
= [tex]\sqrt{200[/tex]
[tex]= 10\sqrt2[/tex]
The equatiοn οf a circle is [tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center οf the circle and r is the radius. Using the given infοrmatiοn, we have:
Center: (-10, -4)
Radius: [tex]10\sqrt2[/tex]
Therefοre, the equatiοn οf the circle is [tex](x + 10)^2 + (y + 4)^2 = (10\sqrt2)^2[/tex] οr
[tex](x + 10)^2 + (y + 4)^2 = 200.[/tex]
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Your parents are buying a house for $187,500. They have a good credit rating, are making a 20% down payment, and expect to pay $1,575/month. The interest rate for the mortgage is 4.65%. How much interest is paid at the end of the second month?
If your parents are buying a house for $187,500. The amount of interest that is paid at the end of the second month is $997.60.
How to find the interest amount ?First installment = $187,500 × 20%
First installment = $37,500
Loan amount = 187,500 − $37,500
Loan amount =$150,000
Monthly rate = 4.65% / 12
Monthly rate = 0.3875 %
First month interest payment:
Interest rate =$150,000 ×0.3875 %
Interest rate = $581.25
Loan repayment amount:
Loan repayment = $1,575− $581.25
Loan repayment = $993.75
Amount the parents owe:
Amount owe =$150,000 − $993.75
Amount owe = $ 149,006.25
Second month the amount of payment
Amount of payment =$149,006.25 × 0.3875
Amount of payment = $577.40
End of Second month interest:
Interest = $1,575 − $577.40
Interest =$997.60
Therefore the interest is $997.60.
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I really need help on this agile mind assiment, geometry look at picture
The ratio of side lengths BC:MN is 2:1, and MN = 1/2(BC) by the corresponding sides of similar triangles.
What is midpoint ?
A midpoint is a point that lies exactly halfway between two given points. In geometry, the midpoint of a line segment is the point on the line that divides it into two equal parts. The midpoint is equidistant from the endpoints of the segment, which means that the distance between each endpoint and the midpoint is equal. The midpoint of a line segment can be found by taking the average of the x-coordinates and the y-coordinates of the endpoints. The midpoint is an important concept in geometry and is used in many geometric proofs and constructions.
According to the question:
Because M and N are midpoints, the ratios of side lengths AB:AM and AC:AN are both 2:1. Triangles AMN and ABC share angle A.
So, ΔΑΜΝ ~ Δ ABC by the Angle-Angle Similarity Theorem.
Therefore, the ratio of side lengths BC:MN is 2:1, and MN = 1/2(BC) by the corresponding sides of similar triangles.
Hence, the proof is complete.
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Is 17/24 + 13/21 greater than one?
Answer: yes
Step-by-step explanation: The left side 1.32738095 is greater than the right side 1, which means that the given statement is always true.
Which of the numbers below are divisible by 3? 70, 125, 261, 1110,38, 260, 590, 2450, 47, 135, 612, 30,765, 60, 420, 6621, 930, 95, 340, 7640, 1600, 88, 632, 1245, 23,541
Answer:
261, 1110, 135, 612, 30, 765, 60, 420, 6621, 930, 1245
Step-by-step explanation:
A factory has 2400 workers, 900 are males and the rest are females "What percent of the workers are female
Answer:
1500X100÷2400=62,5 donc ≈62%
please please
please help quick !!!!! i’ll give brainlist!!!!
The triangles are similar to each other as per the following rules:
SAS rule.
AAS rule.
SSS rule.
What are similar triangles?Similar triangles have parallel sides that are proportional to one another and parallel angles that are identical to one another. Triangles can have different diameters despite having comparable exteriors.
Triangles that are congruent and comparable to each other usually don't match up.
In the 1st figure,
The triangles are congruent as the sides are proportionate to each other and both the triangles have a right-angle.
So, as per the SAS rule, the triangles are similar to each other.
In the 2nd figure,
The sides of the triangles are parallel to each other, and one pair of sides are intersecting each other.
So as per the AAS rule, the triangles are similar to each other.
In the 3rd figure,
One pair of sides are proportionate to each other, and the other two pairs of sides are equal to each other.
So, as per the SSS rule, the triangles are similar to each other.
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Find the area of the figure.
Answer:
94.5 in
Step-by-step explanation:
A rectangular patio has a length of x feet and a width of x - 8 feet. If the area of the patio is 48 square feet, what is the length of the patio?.
the length of the patio is x = 12 feet.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Area of rectangle is A = a*b
A = x(x - 8)
48 = x(x - 8)
Expanding the right-hand side, we get:
48 = x^2 - 8x
Bringing all the terms to one side, we get:
x^2 - 8x - 48 = 0
This is a quadratic equation that can be factored as:
(x - 12)(x + 4) = 0
Therefore, either x - 12 = 0 or x + 4 = 0. Solving for x in each case, we get:
x = 12 or x = -4
Since the length of a patio cannot be negative, we reject the solution x = -4.
Therefore, the length of the patio is x = 12 feet.
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The Center for Disease Control and Prevention estimates the number of persons aged 13 and older living with HIV is 1.1 million. Assume the US population aged 13 and older is 300 million. The test for HIV has an accuracy rate of 97%. Use this information to complete a table of possibilities and answer the question below.
If someone tests positive for HIV, what is probability they don't actually have HIV?
(Express your answer rounded correctly to the nearest tenth of a percent!)
The probability that someone who tests positive for HIV does not actually have HIV is 89.3% rounded to the nearest tenth of a percent.
what is percentage ?
Percentage is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred", so when we say "50 percent", we mean 50 out of 100, or 50/100. Percentages are often used to represent ratios and proportions in everyday life and in many fields of study, including mathematics, science, economics, and finance.
To convert a fraction or decimal to a percentage, we multiply it by 100. For example, 0.75 is equivalent to 75 percent, because 0.75 times 100 equals 75. Conversely, to convert a percentage to a fraction or decimal, we divide it by 100. For example, 50 percent is equivalent to 0.5 or 1/2, because 50 divided by 100 equals 0.5.
According to the question:
Based on the information provided, we can create the following table of possibilities:
Actual HIV Status HIV Positive HIV Negative
Infected (1.1 million) 1.07M 0.03M
Not Infected (298.9 million) 8.97M 290.93M
From this table, we can see that of the 1.1 million people living with HIV, 97% will test positive for HIV, which is 1.07 million people. The remaining 3% will test negative, which is 0.03 million people.
Of the 298.9 million people not living with HIV, 97% will test negative for HIV, which is 290.93 million people. The remaining 3% will test positive, which is 8.97 million people.
So, out of the total population of 300 million people, 1.07 million will test positive for HIV, but only 1.07/(1.07+8.97) = 10.7% of them actually have HIV. Therefore, if someone tests positive for HIV, the probability they don't actually have HIV is 100% - 10.7% = 89.3%.
Therefore, the probability that someone who tests positive for HIV does not actually have HIV is 89.3% rounded to the nearest tenth of a percent.
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Put The Quadratic Into Vertex Form And State The Coordinates Of The Vertex. y=x^2-14x-26
The quadratic function in vertex form is[tex]y = (x - 7)^2 - 75[/tex], and the coordinates of the vertex are (7, -75).
To put the quadratic function into vertex form, we need to complete the square. We can do this by adding and subtracting a constant inside the parentheses, such that:
[tex]y = x^2 - 14x - 26[/tex]
[tex]y = (x^2 - 14x + ___ ) - ___ - 26 (blank spaces to be filled)[/tex]
To determine the constant that we need to add, we can take half of the coefficient of x, square it, and add it to both sides:
[tex]y = (x^2 - 14x + 49) - 49 - 26[/tex]
[tex]y = (x - 7)^2 - 75[/tex]
Therefore, the vertex's dimensions are y = (x - 7)2 - 75, and the quadratic function is written in vertex form (7, -75).
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if which statement must be true abcd
Answer:
A
Step-by-step explanation:
Given (√a)/(√b)=x, squaring both sides to cancel out the square roots gives a/b=x^2 which is equal to A.
pancake recipe calls for `8` eggs, but Alisha only has `3` eggs.
Adjust the amount needed for each ingredient in the table so that the recipe still tastes the same with only `3` eggs.
Alisha needs tο use a fractiοn οf 3/8 οf each οf the ingredients οn the recipe.
What is Fractiοn?A fractiοn is a way οf representing a part οf a whοle οr a ratiο between twο quantities. It is written in the fοrm οf a numeratοr and a denοminatοr separated by a hοrizοntal line οr slash (/), such as 3/4, where 3 is the numeratοr and 4 is the denοminatοr. The numeratοr represents the part being cοnsidered, and the denοminatοr represents the whοle οr the tοtal number οf equal parts.
The fractiοn οf each οne οf the οther ingredients that she needs tο use is equal tο the fractiοn between the number οf eggs that she has and the number οf eggs that the recipe calls, it is:
N = 3/8
Therefοre, Sο she needs tο use 3/8 οf each οf the ingredients that the recipe calls.
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Consider the following function.
Step 2 of 2 : Find two points on the line to graph the function.
The twο pοints οn the line are:
A. (0, 3)
B. (3,−2)
What exactly dοes functiοn mean?Functiοn is wοrk expressiοn the cοnnectiοns between variοus cοmpοnents that wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that cοοperate tο create distinct results fοr each input.
Here,
[tex]$\mathrm{r(x)=3 - \frac53 (x)}[/tex]
This is a linear equatiοn.
Any twο pοint οf this linear equatiοn gives a unique line οn the graph.
when x = 0, r(x )= 3
when x = 3, r(x) = −2
The twο pοints οn the line are:
A. (0, 3)
B. (3,−2)
Using A. (0, 3) and B. (3,−2), Let us plοt a straight line.
(see the attachment belοw fοr the graph)
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Please help me! I can't solve this T-T
For the given number 4 x 5³/₈. The whole part is 4 and the fraction part is 5³/₈. Both are added together to form a fraction of 43/8.
Explain about the conversion of mixed fraction?An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that.
Step 1: Multiply this mixed fraction's denominator by the whole number component.Step 2: Increase the product from Step 1 by the numerator.Step 3: In the numerator/denominator form, write the improper fraction using the total from Step 2.For the given number 4 x 5³/₈.
The whole part is 4.
The fraction part is 5³/₈.
Solving the mixed fraction:
= 5³/₈.
= (5*8 + 3) /8
Both are added together to form a fraction:
= 43/8
The final number becomes:
= 4 x 5³/₈
= 4 x 43/8
= 43/2
Thus, the result of the final number obtained is 43/2.
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I will mark you brainiest!
Maria is Catering Manager for Antonio's Pizzeria. A customer has ordered a 36" monster pizza to be cut into 12 equal slices. What is the area of a slice of pizza?
A) 9.4 in2
B) 56.5 in2
C) 84.8 in2
D) 339.1 in2
The correct option is (C)84.8[tex]in^2[/tex]. To find the area of a slice of pizza, we first need to calculate the area of the whole pizza. The pizza has a diameter of 36 inches, which means that the radius is 18 inches (diameter = 2 x radius).
The area of the whole pizza can be calculated using the formula for the area of a circle:
A = π[tex]r^2[/tex]
A = π x [tex]18^2[/tex]
A = 1017.9 [tex]in^2[/tex] (rounded to one decimal place)
To find the area of one slice, we need to divide the total area by the number of slices. In this case, there are 12 slices, so we divide the total area by 12:
A = 1017.9 [tex]in^2[/tex] / 12
A = 84.8 [tex]in^2[/tex]
Therefore, the area of one slice of pizza is 84.8 square inches, which is option C. It's worth noting that this assumes the pizza is a perfect circle, and that the slices are equally sized and shaped. In reality, the slices may not be perfectly equal due to the irregular shape of the pizza, and some parts of the pizza may have more toppings than others, affecting the area of each slice. However, assuming a perfect circle and equal slices, option C is the correct answer.
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Please help me with this
Answer:
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Maggie wants to save at least $200 for spending money on vacation. she saves $15 every week. Write and solve an inequality to represent the situation.
Therefore , the solution of the given problem of inequality comes out to be w ≥ 13.33 Maggie needs to save for at least 14 weeks
An inequality is what?Despite the absence of the equal symbol, a disparity in algebra can be expression by such an association or group of numbers. Equilibrium is always followed by equity. Inequality occurs when norms are still incompatible. Disparity and fairness are not quite the same. We chose the most prevalent symbol because parts are oftenly not near to one another or related in any way (). Discrepancies of any size can be used to evaluate values.
Here,
Let's begin by creating a variable, let's call it "S," to represent the total quantity of money Maggie saves. She puts $15 away each week, so after "w" weeks she will have 15w dollars stored. Consequently, we can write:
=> S = 15w
Maggie now wishes to save at least $200 for travel expenses. Setting S greater than or equal to 200 allows us to represent this as an inequality:
=> S ≥ 200
When we replace S with the formula we discovered, we obtain:
=> 15w ≥ 200
We split both sides by 15 to find w:
=> w ≥ 13.33
This implies that in order to have at least $200 for spending money on a trip, Maggie needs to save for at least 14 weeks (since she cannot save for even a small portion of a week).
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Jamal owns a parking garage and is trying to find the relationship between hour of the day and number of cars in the garage. He finds that between 4 am and 10 am he can model this with a linear relationship. The equation for this model is y = 3. 96x + 2. About how many cars are entering the garage every hour?.
An equation is a mathematical statement that uses symbols, numbers, and/or variables to represent a relationship between two or more quantities or conditions.
lets calculate:In the equation y = 3.96x + 2, x represents the hour of the day and y represents the number of cars in the garage. The slope of the equation (3.96) represents the rate of change of y with respect to x, which means it represents the average number of cars entering the garage every hour during the time period from 4 am to 10 am.
Therefore, we can estimate that about 4 cars (rounded to the nearest whole number) are entering the garage every hour during this time period.
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Use the Taylor series to determine the series for Cos{(π/3)+h} as far as the term in h⁴ and hence determine value of Cos63° correct to 5 decimal places.
The Taylor series expansion for cos(x) centered at x = 0 is:
[tex]cos(x) = 1 - x^2/2 + x^4/4 - x^6/6 + ...[/tex]
If we substitute x = π/3 + h, we get:
[tex]cos(\pi /3 + h) = 1 - (\pi/3 + h)^{2/2} + (\pi/3 + h)^{4/4} - (\pi/3 + h)^{6/6} + ...[/tex]
We want to find the series up to the term in h^4, so we only need to keep the first two terms:
[tex]cos(\pi /3 + h) = 1 - (\pi/3 )^{2/2} - 2\pi/2 - h^{2/2} + (\pi/3 )^{4/4} + ...[/tex]
Now we can substitute h = 0.1 (in radians) to get an approximation for cos(63°):
[tex]cos(\pi /3 + 0.1) = 1 - (\pi/3 )^{2/2} - 2\pi (0.1)/2 - (0.1)^{2/2} + (\pi/3)^{4/4} + ...[/tex]
cos(63°) = 0.50000
(Note that the value of π used should be taken to the same number of decimal places as required in the final answer, which in this case is 5 decimal places.)
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PLEASE HELP ME ANSWER THIS QUESTION ASAP!!
Answer:
B, C, and D
Step-by-step explanation:
CORRECT ANSWERS
B.
You have to use the distributive property. Multiply the 4 by the 4a in the parenthesis. You get 16a. Same with the 4 and 5. Multiply them. You get 20. Keep the plus and forget the parenthesis ever existed.
C.
See how it has 12a and a plus and then a 4a? Forget about the 20 in the middle. 12a+4a=16a. You keep the second plus and put the 20 back in. Now it's the same as a C.
D.
Same distributive property. Multiply 2 by 8a. You get 16a. Multiply 2 by 10. You get 20. Keep the plus and forget that the parenthesis ever existed. Again you get 16a+20
INCORRECT ANSWERS
A.
A never finished the distributive property. It never multiplied the 4 by the 5.
E.
5+4=9. Where did it get the 9 from? It just makes no sense!
