In drawing the width of park is 17 inches.
what is scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure.
Scale factor is described as the number or the conversion factor which is used to adjust the size of a figure without changing its shape. It is used to expand or decrease the size of an object.
Given:
The scale chosen 1 inch= 3 yards.
Now, the actual width is 51 yards
So, in inch it would be
= 51/3
= 17 inches.
Hence, in drawing the width of park is 17 inches.
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Jim read 24 pages in 40 minutes on Tuesday and 18 pages in 24 minutes on Wednesday. Are the ratios of pages read to minutes on Tuesday and Wednesday proportional?
Explanation: For this question, we just need to represent our proportions by day in form of fractions.
Step 1:
On Tuesday Jim reads 24 pages in 40 mins so we have
[tex]\frac{24}{40}[/tex]On Wednesday Jim reads 18 pages in 24 mins so we have
[tex]\frac{18}{24}[/tex]Step 2: Now all we need to do is to calculate the divisions and compare if they are equal or different
[tex]\begin{gathered} \frac{24}{40}=0.6 \\ \frac{18}{24}=0.75 \\ so\text{ }\frac{24}{40}\ne\frac{18}{24} \end{gathered}[/tex]Final answer: As we can see above both proportions are different so the final answer is that the ratios of pages that Jim reads per minute on Tuesday and Wednesday are not proportional.
QUESTION There are dozens of personality tests available on the World Wide Web (including one that tells the test taker which dead Russian composer he's most like). One test, scored on a scale of 0 to 200, is designed to give an indication of how "personable" the test taker is, with higher scores indicating more "personability" Suppose that 19 classmates have taken this test and scored as follows: 84, 68, 80, 52, 64, 68, 58, 83, 70, 54, 59, 73, 56, 72, 53, 57, 73, 51, 82 C Using the tool provided, construct a box-and-whisker plot for the data.
We need to make a box plot (also known as box-and-whisker) with the following data:
84, 68, 80, 52, 64, 68, 58, 83, 70, 54, 59, 73, 56, 72, 53, 57, 73, 51, 82.
Joe went to the hobby shop and bought 2 model sports cars and spent$8.95 each on some paints. If he spent a total of $23.65, what was the costof each model car?*
Step 1
Find the cost of the 2 model cars
Total cost of two model cars and paint = $23.65
Cost of some paint = $8.95
Cost of 2 model cars = $23.65 - $8.95
= $14.7
Step 2
Calculate cost of each model car
Cost of each model car = $14.7/2
= $7.35
2 4 Number of Hours Number of Samples Left 25 Based on data on the table, which of the following is a TRUE statement? O Initially, supermarket had 85 samples. Initially, supermarket had 105 samples. O Every hour, supermarket distributed 20 samples to its customers. O Every hour, supermarket distributed 5 samples to its customers.
From the given table we can see that as tthe number of hour increases, the number of supermarket samples decreases. This is an inverse proportionality.
Let the time be represented as t;
The number of supermarket samples be s
[tex]\begin{gathered} t\propto\frac{1}{s} \\ t\text{ = }\frac{k}{s} \end{gathered}[/tex]k is the constant of variation
We can see that as the time decreses by 2, the factor inmcreases by 20
Hence at t = 0, the samples will be 20 + 85
Hence at t = 0, the samples will be 105
Hence we can that say that initially, supermarket had 105 samples. Option B is correct
A person places $13900 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 18 years.
The Solution:
Given the formula:
[tex]V=Pe^{rt}[/tex]We are required to find the amount in the account after 18 years.
In this case,
[tex]\begin{gathered} V=\text{ ?} \\ P=\text{ \$13900} \\ r=2.8\text{\%}=0.028 \\ t=18\text{ years} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]V=13900e^{0.028\times18}=23009.078\approx\text{ \$23009.08}[/tex]Therefore, the correct answer is $23009.08
A person stands 5 meters from a building. The angle of elevation to the top of the building is 75°. Find the height of the building to the nearest tenth.
Using the information given in the exercise, you need to draw the following Right triangle (It is not drawn to scale):
Where "h" is the height of the building in meters.
To find the height, you can use the following Trigonometry Identify:
[tex]\tan \alpha=\frac{opposite}{adjacent}[/tex]In this case:
[tex]\begin{gathered} \alpha=75\degree \\ opposite=h \\ adjacent=5 \end{gathered}[/tex]Then, you can substitute values and solve for "h". This is (rounded to the nearest tenth):
[tex]\begin{gathered} \tan (75\degree)=\frac{h}{5} \\ \\ 5\cdot\tan (75\degree)=h \\ h=18.66 \\ h\approx18.7 \end{gathered}[/tex]The answer is:
[tex]18.7\text{ }meters[/tex]7) What is the solution of the system of equations? Show your work y = -5x + 7 y = -2x + 1
ANSWER
x = 2; y = -3
EXPLANATION
We have two equations given:
y = -5x + 7
y = -2x + 1
We can equate both equations because they both yield y.
That is:
-5x + 7 = -2x + 1
Collect like terms:
7 - 1 = -2x + 5x
=> 3x = 6
Divide through by 3:
x = 6/3
x = 2
From the first equation:
y = -5(2) + 7
y = -10 + 7
y = -3
Therefore, the solution to the system of equations is x = 2 and y = -3
4. The student enrollment at a local university is 53% female. Answer the following questionsbased on a sample of 32 randomly selected students.a. What is the probability that 20 of the students sampled are female? (4 pts)b. What is the probability that less than half of the sample is female? (6pts)
Let x be a random variable representing the number of female students enrolled in the university. This is a binomial distribution since there are two outcomes only. The student is either a male or a female
From the information given. the probability that the student is a female is
53/100 = 0.53
Thus, p = 0.53
The probability that the student is not a female, q is 1 - p
Thus, q = 1 - 0.53 = 0.47
a) We want to determine the probability of P(x = 20)
Given that n = 32, from the binomial distribution table,
p(x = 20) = 0.08
the probability that 20 of the students sampled are female is 0.08
b) Half of the sample is 32/2 = 16. The probability that less than half of the sample is a female is expressed as
p(x < 16) = 0.3
the probability that less than half of the sample is female is 0.3
Find the equation of the line with the given properties. Sketch the graph of the line. The line passes through (-1.6,4.4) and is parallel to the x-axis. (Simplify)
Given the point:
(-1.6, 4.4)
Let's find the equation of the line which passes through the given point and is parallel to the x-axis.
Since the line is parallel to the x-axis, the line is a horizontal line located at the y-coordinate of the point.
Therefore, the equation of the line will be:
y = 4.4
To sketch the graph, let's draw a horizontal line that passes through the point: y = 4.
The graph is shown below:
(G.12, a points) A circle has a center at (-6.5) and a radius of 8 units. Create the equation of this circle (x + 6² (y + 5) 42 (y - 5) 82 (x - h) (-k) 72
Information given:
Center at (-6, 5)
Radius= 8 units.
A circle is represented by the following expression:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where, } \\ (h,k)\text{ is th center} \\ r\text{ is the radius} \end{gathered}[/tex]Then, the equation of this circle would be:
[tex](x+6)+(y-5)=8^2[/tex]Given r(x)=x3 - 4x2 +4x -6 find the value of r(2).
Given the function:
[tex]r(x)=x^3-4x^2_{}+4x-6[/tex]We are required to find the value of r(2).
This simply means we must substitute x = 2 wherever we see x in the function r(x).
This is done below:
[tex]\begin{gathered} r(x)=x^3-4x^2+4x-6 \\ \text{substitute x = 2} \\ r(2)=2^3-4(2)^2+4(2)-6 \\ \\ \therefore r(2)=8-16+8-6 \\ r(2)=-6 \end{gathered}[/tex]Therefore, r(2) = -6.
Explanation:
Because when x = 2, r(2) = -6, it means that we can re-write x = 2 as:
[tex]\begin{gathered} x=2 \\ \text{subtract 2 from both sides} \\ x-2=2-2 \\ x-2=0 \end{gathered}[/tex]If r(2) were equal to zero i.e. r(2) = 0, it would have been a factor of r(x). But because
r(2) = -6, it means that (x - 2) divides r(x) and gives a remainder of -6.
Hence, (x-2) divides r(x) and leaves a remainder of -6
Scott mows 25 lawns. He took a survey to see how many people are satisfied with his services and found that 85% thought he did a good job or better. About how many people were not satisfied with Scott’s work
Given that Scott mows 25 lawns and 85% thought he did a good job or better.
the percentage of those that are not satisfied with his job is;
[tex]100-85=15\text{\%}[/tex]The number of people that are not satisfied with his job is;
[tex]\begin{gathered} n=15\text{\% of 25}=0.15\times25 \\ n=3.75 \\ n\approx4 \end{gathered}[/tex]1. Write out a detailed proof of the fact that, given two numbers in scientific notation, a x 10^n and b x 10^n, a < b, if and only if a x 10^n < b x 10^n
A positive B negative C zeroD the parabola opens upE the parabola opens up F the parabola opens down
Solution
Step 1:
The general parabolic function is given as:
[tex]\text{y = ax}^2+bx+c[/tex]If a is positive, the parabola is upward.
If a is negative, the parabola is downward.
Step 2
The c-value is where the graph intersects the y-axis. In this graph, the c-value is -3. The graph of a parabola that opens up looks like this. The c-value is where the graph intersects the y-axis.
Step 3:
Finally, the c-value can also be called the y-intercept of the parabola. Algebraically, this is where the x-value is zero and graphically, this is where the graph intersects the y-axis.
Final answer
The c value of the function represented in the graph is -3 because the parabola opens up.
16. Juan is a real estate agent that receives a 3% commission on each property that he sells. He sold a home to a client that purchased the home for $258,250.00. What was his commission on this home? A.7,748.5 B.7,748 C.7,747 D.7,748.50
We need to calculate how much is 3% out of $258,250.00. (the cost of the home).
To calculate any percentage, what we need to do is divide the quantity by 100, and multiply the result by the percentage we want. In this case:
[tex]\frac{$258,250$}{100}\times3[/tex]divide $258,250 by 100 and multiply by 3.
the result of this will be:
[tex]\frac{$258,250$}{100}\times3=7,747.5[/tex]Answer: 7
2. The movie shop sells posters for $7, DVDs for $15, and CDs for $9. Write 20 points an algebraic expression to represent the total cost for 2 posters, d DVDs, and c CDs.
According to the information given in the exercise, you know that "d" represents the number DVDs and "c" represents the number of CDs.
Using the information given in the exercise, you know that the cost for "d" DVDs sold can represented as:
[tex]15d[/tex]And the cost of "c" CDs sold can be represented as:
[tex]9c[/tex]You also know that the cost of 2 posters of $7 each, is:
[tex]2(7dollars)=14dollars[/tex]Then, you can identify that the total cost for 2 posters, "d" DVDs and "c" CDs can be found by adding all the costs. Therefore, you can write the following expression to represent this:
[tex]2(7)+15d+9c[/tex]If you simplify it, you get:
[tex]=14+15d+9c[/tex]The answers are: First option and Second option.
Carson wants to use a sheet of fiberboard 29 inches long to create a skateboard ramp with a 19∘angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary.
The length of the highest point is 9.98 inches.
What is the height?We know that the angle of elevation is the angle that the ramp makes with the ground. Recall that in order to solve thus problem we would have to refer to the geometry of the right angled triangle in this case.
Given that;
tan 19 = opposite/ adjacent
Adjacent = 29 inches long
Opposite = ??
Opposite = 29 tan 19
= 9.98 inches
We can see that the length of the highest part of the ramp from the calculations that we have just made is obtained as 9.98 inches.
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Prealgebra- Determine whether the lines passing through the pairs of points are parallel, perpendicular, or neither
It is important to note the following:
• If the slopes of the two lines are equal, they are parallel.
,• If the slopes of the two lines are negative reciprocal of each other, they are perpendicular.
Let's now calculate the slope of each line. Use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's start with line 1.
[tex]m=\frac{1-13}{-8-1}\Rightarrow m=\frac{-12}{-9}\Rightarrow m=\frac{4}{3}[/tex]The slope of line 1 is 4/3.
Let's move on to line 2.
[tex]m=\frac{\frac{5}{3}-(-1)}{5-3}\Rightarrow m=\frac{\frac{8}{3}}{2}\Rightarrow m=\frac{4}{3}[/tex]The slope of line 2 is also 4/3.
Since the slopes of the two lines are the same, then the two lines are parallel.
pls help me and no fake answer i really need help :(Show that the volume of the solid of revolution formed by revolving the region bounded by the graph of f(x) = (3x+5)^3, x =0 and x = 1 about the x-axis is 1/21 (8^7 -5^7) pi unit^3
Solution
Given the function
[tex]f(x)=(3x+5)^3[/tex]If we graph the equation, we would have.
when x = 0, f(x) = 5^3 = 125
when x = 1, f(x) = 8^3 = 512
Hence, the solid of revolution is given by
[tex]V=\pi\int_0^1(3x+5)^6dx[/tex]Evaluating the integral
[tex]\begin{gathered} V=\frac{\pi}{7\times3}[(3x+5)^7]\text{ from 0 to 1} \\ \\ \end{gathered}[/tex][tex]\Rightarrow V=\frac{\pi}{21}(8^7-5^7)\text{ unit}^3[/tex]Which formula do I use and how do I key it in on my calculator
Modeling population growth:
Being Po the initial population, K the carrying capacity (or maximum capacity), and r the growth rate, The model for the population at a time t is:
[tex]P(t)=\frac{K}{1+\left(\frac{K-P_o}{P_o}\right)e^{-rt}}[/tex]For the problem, we are given Po = 300, r = 40% = 0.4, K = 3600. Substituting, we get the model:
[tex]P(t)=\frac{3600}{1+\left(\frac{3600-300}{300}\right)e^{-0.4t}}[/tex]Operating:
[tex]P(t)=\frac{3600}{1+11e^{-0.4t}}[/tex]For t = 4 years:
[tex]P(4)=\frac{3600}{1+11e^{-0.4\times4}}[/tex]Calculating:
P(4) = 1118
Answer: 1118 trout
Note: The result above was rounded to the nearest whole number
Finding roots -2x^2+11×-12
The roots of the given expression -2x² + 11x - 12 is found as 4 and 3/4.
What is termed as the root of equation?The values of x that satisfy a provided quadratic equation ax2 + bx + c = 0 are known as its roots. They are, in other words, the qualities of the variable (x) that satisfy the equation. The roots of the a quadratic function are indeed the x-coordinates of the function's x-intercepts. Because the degree of such a quadratic equation is two, it can only have two roots.For the given equation;
-2x² + 11x - 12
To find the roots, put equation equals zero.
-2x² + 11x - 12 = 0
Divide equation with -1.
2x² - 11x + 12 = 0
Break the number(2×12 = 24) such that their addition will be -11 to find the factors.
2x² - 8x - 3x + 12 = 0
Taking 2x common from first two terms and -3 common from last two terms.
2x(x - 4) - 3(x - 4) = 0
Taking (x -4) common from both terms.
(x - 4)(2x - 3) = 0
Equating each.
x = 4 and x = 3/4
Thus, the roots of the given expression is found as 4 and 3/4.
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sketch and label a net of this pizza box it has a square top that measures 16 inches on a side and the height is 2 inches
The net of a pizza box with sides 16 inches by 16 inches and a height of 2 inches;
Come up with a set of 6 values that have a standard deviation of 2.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question
STEP 1: Write the formula for Standard Deviation
[tex]\begin{gathered} \sigma={\sqrt{\frac{\sum(x_{i}-{\mu})^{2}}{N}}} \\ \text{where }\sigma\text{ is the standard deviation} \end{gathered}[/tex]STEP 2: Find the set of 6 values that have a standard deviation of 2
Using Graphing calculator, this involves testing a set of numbers that has a standard deviation of 2
Using the set of numbers below:
[tex]\begin{gathered} A=1,2,3,4,5,6 \\ \text{Standard deviation using graphing calculatore gives }1.87082869339 \\ \text{This comes close to 2 and the numbers in the set can be tweaked to reach a standard deviation of 2} \end{gathered}[/tex]Tweaking the set of values to the one below:
[tex]\begin{gathered} A=1,2,5,5,5,6 \\ \text{Standard deviation using graphing calculatore gives }2 \end{gathered}[/tex]Hence, the set of 6 values that have a standard deviation of 2 are 1,2,5,5,5,6
Step-by-step explanation:
the stages deviation is the square root of the sum (divided by the number of data points) of the squared differences of each individual data point from the mean value.
so, we need to calculate backwards.
to get the standard deviation to be 2, then the square of 2 (4) is the sum of all squares differences divided by 6 (as we need to find 6 values).
4 = sum(diff²) / 6
so the sum of all squared differences from the mean value is 4×6 = 24.
so, we have 6 squared differences.
that means the simplest approach would be to say that each squared difference is 24/6 = 4
and then each difference from the mean value is
sqrt(4) = 2.
that's means we need to find 6 numbers with a mean value that is 2 off of every data point.
e.g.
2, 2, 2, 6, 6, 6
the mean value is
(2+2+2+6+6+6)/6 = 24/6 = 4
so, every data point has a difference of 2 to the mean value.
and this dataset has a steadfast deviation of 2.
The equations of 2 lines are shown below. 2x - y = 2 3x + 4y = 25 What is the product of (x.y) of the point of intersection?
Question:
The equations of 2 lines are shown below. 2x - y = 2 3x + 4y = 25 What is the product of (x.y) of the point of intersection?
Solution:
Consider the following line equations:
Equation 1
[tex]2x-y\text{ = 2}[/tex]Equation 2:
[tex]3x+4y\text{ = 2}5[/tex]Now, solving equation 1 and equation 2 for the variable y, we get:
Equation 3:
[tex]y\text{ = 2x-2}[/tex]and
Equation 4:
[tex]y\text{ = -}\frac{3}{4}\text{x +}\frac{25}{4}[/tex]now, if we relate equations 3 and 4 we obtain:
[tex]2x-2\text{ = -}\frac{3}{4}\text{x +}\frac{25}{4}[/tex]this is equivalent to:
[tex]2x\text{ + }\frac{3}{4}x\text{ = }\frac{25}{4}+2[/tex]this is equivalent to:
[tex]\frac{11}{4}x\text{ = }\frac{33}{4}[/tex]this is equivalent to:
[tex]11x\text{ = 33}[/tex]this is equivalent to:
[tex]x\text{ = }\frac{33}{11}=\text{ 3}[/tex]then:
[tex]x\text{ = 3}[/tex]now, replacing this in equation 3, we get:
[tex]y\text{ = 2(3)-2 = 6-2 = 4}[/tex]thus
[tex]y\text{ = 4}[/tex]Thus the point of the intersection is (x,y) = (3,4) and we can conclude that the product of x = 3 and y = 4 is :
[tex]x\text{ . y = 3 . 4 = 12}[/tex]phil needs to run at least 30miles30miles this weekweek for his training if he has already ran a⋅18milesa⋅18miles as we've been how many milesmiles should you run on each of the 33 remaining dayday this week
answer: 4 miles per day
The world population in 1993 is projected to be billion people.
EXPLANATION
The growth model is given by the following expression:
[tex]A=A_0(1+r)^t[/tex]Where A_0=Initial Population = 5 billion
r=growth rate = 2% = 0.02 in decimal form
t=time = 1993 - 1987 = 6 years
Plugging in the numbers into the equation:
[tex]A=5(1+0.02)^6[/tex]Computing the power:
[tex]A=5\cdot(1.02)^6[/tex]Computing the product:
[tex]A=5\cdot1.13[/tex]Multiplying numbers:
[tex]A=5.63billion[/tex]In conclusion, the population in 6 years will be of 5.63 billion.
To amend a country's constitution, 2/9 of the 60 states in that country must approve the amendment. If 14 states approve an amendment, will the constitution be amended?
1) If it's necessary 2/9 of 60 states, then it is a multiplication:
2/9 x 60 = 40/3 =13.333 or 13 3/9 ≅ 13
2) So, yes if 14 states approve it the constitution will be amended.
Mikey's family is taking a road trip. Their car can travel no more than 260 miles without needing to refill the gas tank. They have traveled 112 miles since they last filled the gas tank.Mikey knows that the inequality representing this situation is 112+x≤260.Select from the drop-down menu to correctly interpret the solution of this inequality.Mikey's family can drive Choose... more miles before they need to refill the gas tank.
148 more miles before they need to refill the gas tank.
1) Considering that the inequality that represents this situation is:
[tex]112+x\leq260[/tex]Notice that in this equation "x" stands for the number of miles that he needs to finish the trip.
2) So we can solve that to find out the number of miles Mikey's family can make with the gas already in the car:
[tex]\begin{gathered} 112+x\leq260 \\ 112-112+x\leq260-112 \\ x\leq148 \end{gathered}[/tex]Note that we have subtracted 112 from both sides.
3) Hence, the answer is:
Mikey's family can drive up to 148 miles before they need to refill the gas tank
What is the measure of y?327LYZNХy = [?]Give your answer in simplest form.I
Given:
The length of the triangle is: 27, 3, x, y, and z.
Find: Value of "y"
Sol:
In triangle ACD is:
Use Pythagoras theorem:
[tex]\text{ Hypotenuse}^2=\text{ Base}^2+\text{ Perpendicular}^2[/tex]Apply for triangle ACD then:
[tex]\begin{gathered} AC^2=AD^2+CD^2 \\ \\ (27+3)^2=z^2+x^2 \\ \\ 30^2=z^2+x^2...........(1) \end{gathered}[/tex]
In triangle CBD
Apply theorem then:
[tex]x^2=27^2+y^2.........(2)[/tex]In Triangle ABD
Apply theorem then:
[tex]\begin{gathered} z^2=3^2+y^2...........(3) \\ \end{gathered}[/tex]From eq (2) and eq(3) put the value in eq(1) then:
[tex]\begin{gathered} 30^2=z^2+x^2 \\ \\ 30^2=3^2+y^2+27^2+y^2 \\ \\ 900=9+2y^2+729 \\ \\ 900-(729+9)=2y^2 \\ \\ 162=2y^2 \\ \\ y^2=\frac{162}{2} \\ \\ y^2=81 \\ \\ y=9 \end{gathered}[/tex]So the value of "y" is 9.
Two pools are being drained. To start, the first pool had 3650 liters of water and the second pool had 4166 liters of water. Water is being drained from the first pool at a rate of 27 liters per minute. Water is being drained from the second pool at a rate of 39 liters per minute.Let x be the number of minutes water has been drained.(Photo includes Questions)
The first pool has 3650 liters of water.
The second pool has 4166 liters of water.
It is also given that water drained from first pool at a rate of 27 liters per minute.
The water drained from the second pool at a rate of 39 liters per minute.
Explanationa. Let the x be the number of minutes water has been drained.
The amount of water in the first pool in liters
[tex]3650-27x[/tex]The amount of water in the second pool in liters
[tex]4166-39x[/tex]b. To determine the equation when both the pools has same amount of water.
[tex]\begin{gathered} 3650-27x=4166-39x \\ 39x-27x=4166-3650 \\ 12x=516 \\ x=43 \end{gathered}[/tex]Answera. The amount of water in first pool in liters is 3650-27x.
The amount of water in second pool in liters is 4166-39x.
b. The equation when both the pools has same amount of water is x=43.