We have a right triangle (one of its angle is a 90 degrees angle).
We know that
In the first week of July, a record 1,040 people went to the local swimming pool. In the second week,125 fewer people went to the pool than in the first week. In the third week,135 more people went to the pool than in the second week. In the fourth week,322 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
By the concept of percentage there is 20% decrease in the number of people who went to the pool over these four weeks.
What is percentage?A percentage is a statistic or ratio that is expressed as a fraction of 100 in mathematics. But even though the abbreviation "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to signify it. A % is a dimensionless number; there is no specific unit of measurement for it. %, a relative figure signifying hundredths of any amount. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. A percentage is a figure or ratio that in mathematics represents a portion of one hundred. It is frequently represented by the sign "%" or just "percent" or "pct." For instance, the fraction or decimal 0.35 is comparable to 35%.
In July:
First week:
Number of people went to the local swimming pool
=1040
Second week:
110 fewer people went to the pool than in the first week
Number of people went to the local swimming pool
=1040 - 110
=930
Third week:
130 more people went to the pool than in the second week
Number of people went to the local swimming pool
=930 + 130
=1060
Fourth week:
228 fewer people went to the pool than in the third week
Number of people went to the local swimming pool
=1060 - 228
=832
Decrease in number of people over four week
= number of people in first week - number of people in fourth week
Decrease in number of people over four week
=1040 - 832
=208
Now, the percentage
= 20%
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What is the radius of Earth, in meters, written as a single-digit number multiplied by a power of 10?
Given:
The Radius of earth = 6,378,100 meters
To find:
The radius of earth in single-digit number multiplied by power of 10.
Step by step solution:
R = 6,378,100 meters
R = 6.3781 × 10^6
From here we have calculated the value of the radius in terms of single digit number.
Does the point (–48, –47) satisfy the equation y = x − 1?
To find the answer to the question, we will substitute "-48" into "x" and "-47" into "y" and see if the equation holds true or not.
[tex]\begin{gathered} y=x-1 \\ -47\stackrel{?}{=}-48-1 \\ -47\neq-49 \end{gathered}[/tex]Thus, the point (-48, -47) does not satisfy the equation y = x - 1.
AnswerNoQuestion 2 - Minimum Hours f. In the previous question, if Leah babysits for 7 hours this month, what is the minimum number of hours she would have to work at the ice cream shop to earn at least $120? Justify your answer. (4 POINTS) Give your answer to the nearest whole hour.
Leah earns 5x + 8y dollars, after x hours babysitting and y hours at the ice cream shop.
She wants to earn at least $120, then:
5x + 8y ≥ 120
Given that Leah babysits for 7 hours, then:
5(7) + 8y ≥ 120
35 + 8y ≥ 120
8y ≥ 120 - 35
8y ≥ 85
y ≥ 85/8
y ≥ 10.625
She must work at least 11 hours
Given that 7 + 11 = 18, then she would not work more than 20 hours as she expected
As smart phones have grown in popularity, regular cell phones have fallen out of favor. As aresult, one electronics retailer estimates that 20% fewer regular cell phones will be sold everyyear. If the retailer sells 605,390 regular cell phones this year, how many will be sold 3 yearsfrom now?If necessary, round your answer to the nearest whole number.
309960
Explanation
exponential decay function is a function that shrinks at a constant percent decay rate. The equation can be written in the form
[tex]\begin{gathered} y=a(1-b)^x \\ \text{where a is the initial cost} \\ b\text{ is the decrease percnetage ( in decimal)} \\ x\text{ is the time} \end{gathered}[/tex]so
Step 1
Let
[tex]\begin{gathered} a=605390 \\ b=20\text{ = 0.2} \\ x=\text{ 3 ( years)} \end{gathered}[/tex]replace
[tex]\begin{gathered} y=a(1-b)^x \\ y=605390(1-0.2)^3 \\ y=605390(0.8)^3 \\ y=605390(0.512) \\ y=309959.68 \\ \text{rounded to the whole number} \\ y=309960 \end{gathered}[/tex]therefore, the answer is
309960
I hope this helps you
For each value of w, determine whether it is a solution to w < 9.Is it a solution?W5?YesNo75914
Answer: 5 and 7
Explanation:
we need to determine if a number is a solution to
[tex]w<9[/tex]That reads as "w is less than 9, and not equal to 9"
so we find in our options wich ones are less than 9. The options are:
• 7
,• 5
,• 9
,• 14
The ones smaller or less than 9 are: 5 and 7
The ones greater than 9 or equal to 9 (the ones that are not the solution) are: 9 and 14.
So the solutions are: 5 and 7
I need the answer to number 2 please answer it like the paper so that I can understand it better. Please
Elijah made an error of subtracting the numbers and not including the imaginary sign (letter i)
The correct midpoint is (6, 3i)
Explanation:The two points are 8 + 4i and 4 + 2i
Elijah got the midpoint as (2, 1).
To determine Elijah's error, let's calculate the midpoint of a complex number:
[tex]\text{Midpoint = (}\frac{a\text{ + b}}{2}),\text{ (}\frac{c\text{ + d}}{2})i[/tex]let 8 + 4i = a + ci
let 4 + 2i = b + di
The real numbers will be added together. The imaginary numbers will also be added together.
substituting the values in the formula:
[tex]\begin{gathered} \text{Midpoint = (}\frac{8\text{ + 4}}{2}),\text{ (}\frac{4\text{ + 2}}{2})i \\ \text{Midpoint = }\frac{12}{2},\text{ }\frac{6}{2}i \\ \\ \text{Midpoint = (6, 3i)} \end{gathered}[/tex]Elijah made an error of subtracting the numbers. Also Elijah didn't include the letter representing the imaginary numbers (i).
The correct midpoint is (6, 3i)
Let Iql = 5 at an angle of 45° and [r= 16 at an angle of 300°. What is 19-r|?13.00 14.2O 15.518.0
As given that:
[tex]|q|=5[/tex]At angle of45 degree
and |r| = 16 at 300 degree
so the |q| at 300 degree is:
[tex]\begin{gathered} |q|=5\times\frac{300}{45} \\ |q|=33.33 \end{gathered}[/tex]Now |q-r| is:
[tex]\begin{gathered} |q-r|=33.33-16 \\ |q-r|=17.33 \\ |q-r|\approx18 \end{gathered}[/tex]So the correct option is d.
Geometry Question: Given segment EA is parallel segment DB, segment EA is congruent to segment DB, and B is the mid of segment AC; Prove: segment EB is parallel to segment DC (reference diagram in picture)
Construction: Join ED.
The corresponding diagram is given below,
According to the given problem,
[tex]\begin{gathered} AE=BD \\ AE\parallel BD \end{gathered}[/tex]Since a pair of opposite sides are parallel and equal, it can be claimed that quadrilateral ABDE is a parallelogram.
Then, as a property of any parallelogram, it can be argued that,
[tex]\begin{gathered} AB=DE \\ AB\parallel DE \end{gathered}[/tex]Given that B is the mid-point of AC,
[tex]\begin{gathered} AB=BC \\ AB\parallel BC \end{gathered}[/tex]Combining the above two results,
[tex]\begin{gathered} BC=DE \\ BC\parallel DE \end{gathered}[/tex]It follows that ABCD also forms a parallelogram.
Again using the property that opposite sides of a parallelogram are equal and parallel. It can be claimed that,
[tex]\begin{gathered} EB=DC \\ EB\parallel DC \end{gathered}[/tex]Hence proved that segment EB is parallel to segment DC,
[tex]\vec{EB}=\vec{DC}[/tex]ASGC is also considering adding tennis racquets to the product lines it produces. This would require a $500,000 modification to its factory as well as the purchase of new equipment that costs $1,600,000. The variable cost to produce a tennis racquet would be $55, but John thinks that ASGC could sell the racquet at a wholesale price of $75. John thinks that if ASGC sells the racquet at a lower price, many other retailers might decide to carry it. However, the vice president of ASGC thinks that the tennis racquet is a superior product and that ASGC should sell it for $99.99 to upscale country clubs only. The higher price would give a prestige image. Questions based on the above (10 pts)7. If ASGC produces tennis racquets, how many racquets must it sell at $75.00 and $99.99 to break even? •Breakeven units at 75.00 _______________________________. •Breakeven units at 99.99 _______________________________. •Which price do you recommend and why? __________________________
Solution
[tex]undefined[/tex]12 ft-What is the volume of atriangular pyramid that is12 ft tall and has a basearea of 5 square ft?cubic feet
EXPLANATION:
Given;
We are given a triangular pyramid with the following dimensions;
[tex]\begin{gathered} Base\text{ }area=5ft^2 \\ Height=12ft \end{gathered}[/tex]Required;
We are required to calculate the volume of this pyramid from the dimensions given.
Step-by-step solution;
The volume of a triangular pyramid is given by the formula;
[tex]Volume=\frac{1}{3}Bh[/tex]Where the variables are;
[tex]\begin{gathered} B=base\text{ }area \\ h=height \end{gathered}[/tex]The volume now will be calculated as follows;
[tex]\begin{gathered} Volume=\frac{1}{3}\times5\times12 \\ \\ Volume=20 \end{gathered}[/tex]Therefore,
ANSWER:
[tex]V=20ft^3[/tex]Volume = 20 cubic feet
vertex, domain and range, and zeros in this parabola, could you tell me them?
The vertex, domain, range and zeros of the parabola are -2, (-∞, +∞), (-2,+∞) and -0.5 and 2.5 respectively.
What is parabola ?Parabola is a curve like shape, in which any point is equal distance from a fix point.
The vertex of the parabola in the given graph is -2.
The domain of parabola is all the possible values of x,
in the given graph, the value of x is from -∞ to +∞
So the domain of parabola is (-∞, +∞)
The range of parabolas is all the values of y corresponding to values of x,
in the graph, the value of y≥-2
The range of parabola is (-2,+∞)
Zeros are values on the x-axis, which are 0.
So there are two zeros, -0.5 and 2.5.
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The ratio between the radius of the base and the height of a cylinder is 2:3. If it's volume is 1617cm^3, find the total surface area of the cylinder.
Solution:
The ratio of the radius to the height of the cylinder is
[tex]2\colon3[/tex]Let the radius be
[tex]r=2x[/tex]Let the height be
[tex]h=3x[/tex]The volume of the cylinder is given below as
[tex]V=1617cm^3[/tex]Concept:
The volume of a cylinder is given below as
[tex]V_{\text{cylinder}}=\pi\times r^2\times h[/tex]By substituting values, we will have
[tex]\begin{gathered} V_{\text{cylinder}}=\pi\times r^2\times h \\ 1617=\frac{22}{7}\times(2x)^2\times(3x) \\ 1617=\frac{22}{7}\times4x^2\times3x \\ 1617\times7=264x^3 \\ \text{divdie both sides by 264} \\ \frac{264x^3}{264}=\frac{1617\times7}{264} \\ x^3=\frac{343}{8} \\ x=\sqrt[3]{\frac{343}{8}} \\ x=\frac{7}{2} \end{gathered}[/tex]The radius therefore will be
[tex]\begin{gathered} r=2x=2\times\frac{7}{2} \\ r=7cm \end{gathered}[/tex]The height of the cylinder will be
[tex]\begin{gathered} h=3x=3\times\frac{7}{2} \\ h=\frac{21}{2}cm \end{gathered}[/tex]The formula for the total surface area of a cylinder is given below as
[tex]T\mathrm{}S\mathrm{}A=2\pi r(r+h)[/tex]By substituting the values, we will have
[tex]\begin{gathered} TSA=2\pi r(r+h) \\ TSA=2\times\frac{22}{7}\times7(7+\frac{21}{2}) \\ TSA=44(7+\frac{21}{2}) \\ TSA=44\times7+44\times\frac{21}{2} \\ TSA=308+462 \\ TSA=770cm^2 \end{gathered}[/tex]Hence,
The total surface area of the cylinder is = 770cm²
Find the z-score location of a vertical line that separates anormal distribution as described in each of the following.a. 15% in the tail on the rightb. 40% in the tail on the leftc. 75% in the body on the rightd. 60% in the body on the left
Answer:
a. z = 1.0364
b. z = -0.2533
c. z = -0.6745
d. z = 0.2533
Explanation:
We can represent each option with the following diagrams
So, for each option, we need to find a z that satisfies the following
a. P(Z > z) = 0.15
b. P(Z < z) = 0.40
c. P(Z > z) = 0.75
d. P(Z > z) = 0.60
Then, using a normal table distribution, we get that each value of z is
a. z = 1.0364
b. z = -0.2533
c. z = -0.6745
d. z = 0.2533
Write the following Equation as a EXPONENTIAL equation do not simplify your answer
Answer:
[tex]V=14^5[/tex]Explanation:
Given the logarithmic equation:
[tex]\log_{14}(V)=5[/tex]The relationship between the logarithm and exponential forms is given below:
[tex]\log_ba=c\implies b^c=a[/tex]That is:
• The base (b) in the logarithmic form becomes the base of the exponent.
,• The answer (c) in the logarithmic form becomes the exponential form.
Thus, the given equation in exponential equation is:
[tex]V=14^5[/tex]Calculate the value of the expression 3x-7 when x = 2
Given:
The expression is,
[tex]3x-7[/tex]To find:
The value when x = 2.
Explanation:
Substitute x = 2 in the given expression, we get
[tex]\begin{gathered} 3(2)-7=6-7 \\ =-1 \end{gathered}[/tex]Thus, the value of the expression when x = 2 is -1.
Final answer:
The value of the expression when x = 2 is,
[tex]-1[/tex]1.For a standard normal distribution, find:P(1.26 < z < 1.48)2.For a standard normal distribution, given:P(z < c) = 0.1288
Standard Normal Distribution
To find the cumulative probability of a Normal Distribution, we need to use some automated digital tool that makes the calculations for us, since it's a pretty complex formula.
We'll use an online tool and provide the results here.
a) P(1.26 < z < 1.48)
The procedure is: Find P(z < 1.48) directly from the tool. Find P(z < 1.48) also. Subtract both values.
P(z < 1.48) = 0.931
P(z < 1.26) = 0.896
Subtract the values above: 0.931 - 0.896 = 0.035. Thus:
P(1.26 < z < 1.48) = 0.035
b) Find c such that: P(z < c) = 0.1288
We need to use the inverse Normal Distribution, enter the probability and find the z-score: c = -1.132
what is 6q - q please
To solve this expression, we just have to subtract because they are like terms
[tex]6q-q=5q[/tex]Hence, the answer is 5q.
Can you please help me out with a question
the figure is composed by a 4 triangles and a cube
to find the area of a triangle we need the base and height. the base is 15ft
to find the height we mut use the pithagorean theorem
h= height of the traingle
[tex]h^2=(15ft)^2+(7.5ft)^2[/tex]resolving we have
[tex]h=\sqrt[\square]{281.25}\text{ = 16.78 aprox}[/tex]and now he have all the measures
each triangle at the top has an area equal to
[tex]A=\frac{16.78ft\cdot15ft}{2}=127.78sq\text{ ft}[/tex]now we multiply that by 4: 127.78sq ft*4=503.1 sq ft
for the bottom part, there are 5 squares of side 15ft
each square has an area = 15ft*15ft = 225 sq ft
multipliying that by 5: 225sqft*5=1125 sq ft
the total area is 1125 sq ft+503.1sqft=1628.1 sq ft rounded is 1628 sq ft
For the volume of the piramid, we use
[tex]V=\frac{1}{3}A\cdot h[/tex]where A is the area of the base and h is the height
so volume of piramid:
[tex]V=\frac{1}{3}\cdot225\text{sqft}\cdot15ft=1125ft^3[/tex]for the volume of the cube we multiply the side length 3 times:
[tex]V\mleft(cube\mright)=(15ft)^3=3375ft^3[/tex]Adding the two volumes:
1125ft^3+3375ft^3=4500 cubic feet
Find the roots of the equation 5x2 + 125 = 0
The given equation is:
[tex]5x^2+125=0[/tex]Divide through by 5
[tex]\begin{gathered} \frac{5x^2}{5}+\frac{125}{5}=\frac{0}{5} \\ \\ x^2+25=0 \\ \end{gathered}[/tex]This is further simplified as:
[tex]\begin{gathered} x^2=-25 \\ \\ \sqrt{x^2}=\pm\sqrt{-25} \\ \\ \sqrt{x^2}=\pm\sqrt{-1}\times\sqrt{25} \\ \\ x^=\pm5i \\ \\ x=5i\text{ and -5i} \\ \end{gathered}[/tex]-Solve the system of equations – X – 8y = 49 and —x – 2y = 7 by combining theequations.
ANSWER
x = 7
y = -7
EXPLANATION
Given:
- x - 8y = 49 ..........(equ 1)
- x - 2y = 7 ............(equ 2)
Desired Outcome
The values of x and y.
Multiply Equation 2 by -1
[tex]equ\text{ 2}\times-1\Rightarrow x+2y\text{ = -7 ............}(equ\text{ 3})[/tex]Add Equation 1 with Equation 3
[tex]\begin{gathered} -\text{ x - 8y = 49} \\ x\text{ + 2y = -7} \\ ------ \\ -6y\text{ = 42} \\ y\text{ = }\frac{42}{-6} \\ y\text{ = -7} \end{gathered}[/tex]Solve for x from equation 3
[tex]\begin{gathered} x\text{ + 2y = -7} \\ x\text{ + 2}(-7)\text{ = -7} \\ x\text{ - 14 = -7} \\ x\text{ = -7 + 14} \\ \text{x = 7} \end{gathered}[/tex]Hence, the values of x and y are 7 and -7 respectively.
The beam of light house makes one complete revolution every 20 seconds how many degrees is it rotate in five seconds
Answer:
Every 5 seconds the beam rotates 90 degrees;
[tex]90^{\circ}[/tex]Explanation:
Given that the beam of a lighthouse makes one complete revolution every 20 seconds.
one complete revolution is;
[tex]360^{\circ^{}}[/tex]The rate of rotation is;
[tex]r=\frac{360^{\circ}}{20}=18^{\circ}\text{ per second}[/tex]The number of degrees it will rotate in 5 seconds is;
[tex]\begin{gathered} x=5\times r=5\times18^{\circ}per\text{ second} \\ x=90^{\circ} \end{gathered}[/tex]Therefore, every 5 seconds the beam rotates 90 degrees;
[tex]90^{\circ}[/tex]9. You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar. Regular withdrawal: $4500 Interest rate: 4.5% Frequency quarterly Time: 24 years Account balance: $
This is a question on Future Value of Annuity. There is a present sum from which withdrawals will be made. We therefore employ the formulae thus:
[tex]PVA=\text{PMT(}\frac{1-(1+\frac{i}{m})^{-mn}}{\frac{i}{m}}\text{)}[/tex]Where:
PVA = Present Value of Annuity
PMT = Periodic sum
i = Interest Rate
n = Number of interest periods
m = Compunding frequency
Substituting, we have:
[tex]\begin{gathered} P\text{VA}=4500(\frac{1-(1+\frac{0.045}{4})^{-(4\times24)}}{\frac{0.045}{4}}) \\ P\text{VA}=263,340 \end{gathered}[/tex]PVA = $263,340
The graph of an inequality has a closed circle at 4.3, and the ray moves to the right. What inequality is graphed?x > 4.3x ≥ 4.3x ≤ 4.3x < 4.3
From the question, we were told that the graph of an inequality has a closed circle at 4.3 and the ray moves to the right also.
We are to determined the inequality that is graphed from the options.
From what is seen, we want x to be greater than or equal to 4.3.
The closed circle tells us that it can be equal to 4.3. The ray to the right tells us that we are looking for numbers larger than 4.3.
So the inequality graphed is that of x is greater than or equal to 4.3
So the correct option is the second option which is x ≥ 4.3.
In general, the y-intercept of the function F(x) = a • bx is the point _____.A.(0, b)B.(0, a)C.(0, x)D.(0, 1)
The y-intercept of a function is the point where the function crosses the y axis and where x = 0
[tex]\begin{gathered} We\text{ are asked to find the y intercept of an exponential function, y = a*b}^x \\ When\text{ x = 0, b}^x\text{ =1 for any value of b} \\ We\text{ are then left with y = a*1 when x =0} \end{gathered}[/tex]The y intercept is therefore given by:
(0,a) --> option B
Suppose tortilla chips cost 32.5 cents per ounce what would a bag of chips cost if it contained 20oz round the answer to the nearest cent
The Solution:
Given:
cost per ounce = 32.5 cents
Required:
To find the cost of a bag of chips that contains 20 oz.
Recall:
ounce = oz
[tex]\begin{gathered} 1\text{ oz}=32.5\text{ cents} \\ \\ 20\text{ oz }=20\text{ ounces} \\ \\ Cost\text{ of 20 oz is :} \\ \\ 20\times32.5\text{ cents=650 cents }=\text{\$}6.50 \end{gathered}[/tex]Therefore, the correct answer is $6.50
Ivanna bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $450 less than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 6.5% per year, and for the laptop it was 9% per year. The total finance charges for one year were $409. How much did each computer cost before finance charges?
Solution:
According to the problem, the laptop costs $450 less than the desktop. Let x the cost of the laptop, then we get the following equation:
[tex]x\text{ + 450 = cost of the desktop}[/tex]now, the total finance charge of $409 is from 9% of the cost of the laptop and 6.5% of the cost of the desktop. According to this, we get the following equation:
[tex]0.09(x)+0.065(x+450)=409[/tex]Applying the distributive property, we get:
[tex]0.09x+0.065x+29.25=409[/tex]now, placing like terms on each side of the equation, we get:
[tex]0.09x+0.065x=409-29.25[/tex]this is equivalent to:
[tex]0.155x\text{ = 379.75}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{379.75}{0.155}=2450[/tex]this means that:
The cost of the laptop is x = 2450
and
The cost of the desktop is x+450 = 2450 +450 = 2900.
So that, we can conclude that the correct answer is:
Cost of the laptop = 2450
Cost of the desktop =2900.
What is the logarithmic form of 9^2=81
Given the equation:
[tex]9^2=81[/tex]Let's write the equation in logarithmic form.
To write in logarithmic form, take the logarithm of base 9 of the right side of the equation equal to the exponent (2).
Thus, we have:
[tex]log_981=2[/tex]Therefore, the logarithmic form of the given equation is:
[tex]log_981=2[/tex]• ANSWER:
[tex]log_981=2[/tex]which table represents points on the graph of h (x) = 3 root -x+2
Given the function :
[tex]h(x)=\sqrt[3]{-x+2}[/tex]To find which table represents the given function, let x with the numbers given in the table and find the corresponding value of h(x)
So, when x = 0
[tex]h(0)=\sqrt[3]{0+2}=\sqrt[3]{2}[/tex]Now look to the tables which table has y = 3root of 2
We can deduce that the first two tables are wrong
Now, substitute with x = 2
[tex]h(2)=\sqrt[3]{-2+2}=\sqrt[3]{0}=0[/tex]So, this result will be agreed with the third table
so, the answer is: Table 3
The area of Square A is 36 square cm. The area of Square A’(A Prime) is 225 ᶜᵐ². What possible transformations did the square undergo?
A possible transformation is a scale. Since the area changed by
[tex]\frac{225}{36}=\frac{25}{4}[/tex]then a possible transformation was a scale by 25/4. A scale by a ratio bigger than one is a dilation.
Then the answer is B.