(Score for Question 3: of 6 points)3. Felipe is ordering new carpet for his bedroom floor. (The floor is represented in the picture below asrectangle JKLM). He knows the base edge, ML, measures 18 ft. And the distance of diagonal KMmeasures 25 ft. What is the area of Felipe's bedroom floor? Show all work and round your answer tothe nearest tenth.JKM
Solution:
Given:
[tex]\begin{gathered} The\text{ length of the room floor is 18 ft} \\ The\text{ width of the room floor is }x \end{gathered}[/tex]
Considering the right triangle KLM,
To get the width (x), we use the Pythagoras theorem.
[tex]\begin{gathered} 18^2+x^2=25^2 \\ x^2=25^2-18^2 \\ x^2=625-324 \\ x^2=301 \\ x=\sqrt{301} \\ x=17.35ft \\ \\ Hence,\text{ the width is 17.35ft} \end{gathered}[/tex]
The area of the bedroom floor is;
[tex]\begin{gathered} A=l\times w \\ A=18\times17.35 \\ A=312.3ft^2 \end{gathered}[/tex]
Therefore, the area of Felipe's bedroom floor to the nearest tenth is 312.3 square feet.
Hello! I need help in answering question number 3 which I will attach. Geometry 3 D shapes. It reads To make one order you need to fill the cone with ice cream first, and then add the scoop on top. How many total cubic inches of ice cream are in one order?
The ice-cream is made up of of a sugar cone and a scoop in the shape of half a sphere
Hence, the formula for the volume V of the total cubic inches of ice cream is:
[tex]\begin{gathered} V\text{ = Volume of cone + half a volume of a sphere} \\ V\text{ = }\frac{1}{3}\pi r^2h\text{ + }\frac{2}{3}\pi r^3 \end{gathered}[/tex]Given:
height of cone = 4.6 inches
radius of cone = 1.7 inches
radius of sphere = 1.7 inches
Substituting the given values:
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\text{ }\times\text{ }\pi\times\text{ 1.7}^2\text{ }\times\text{ 4.6 + }\frac{2}{3}\text{ }\times\text{ }\pi\times\text{ 1.7}^3 \\ =\text{ 24.211 in}^3 \\ \approx\text{ 24.21 in}^3 \end{gathered}[/tex]Answer:
24.21 cubic inches
Emma went to bed at 7:28 p.m. and got up at 6:08 a.m. How many hours and minutes did she sleep?
We will have the following:
First, calcuate the difference in hours:
From 7pm to 6am there are 11 hours.
Then we add the number of minutes, those would be 40 minutes.
So, she slept 11 hours and 40 minutes.
A pie shop bakes a certain amount of pies each week. 150 of those pies are apple pies. These apple pies makes up 40 percent of the total pies. How many pies does the shop make each week?
The number of apple pies made each week is 375
Here, we want to know the total number of pies made per week
Let the total number of pies be p
From the question, 40% of p is 150
Thus, we have it that;
[tex]\begin{gathered} 40\text{ \% of p = 150 } \\ \frac{40}{100}\times\text{ p = 150} \\ 40p\text{ = 100}\times150 \\ \\ p\text{ = }\frac{100\times150}{40} \\ p\text{ = 375} \end{gathered}[/tex]Suppose that you want to buy 6 different books and the order that you buy them does not matter. Then thenumber of ways to choose 6 books from 44 available books is
We have that the order doesn't matter without repetition, so should use combinations that are represented by the next formula:
[tex]C=\frac{n!}{r!(n-r)!}[/tex]Where n is the total of books and r the numbers of the group, in this case, 6 differents books.
Replace these values:
[tex]\frac{44!}{6!(44-6)!}[/tex][tex]C=\frac{44!}{6!(38)!}=7059052\text{ ways to choose 6 books from 44 available}[/tex]The square of the difference between a number n and eighty
Given the statement: The square of the difference between a number n and eighty.
we need to write the algebraic expression for the statement.
The difference between the number n and 80 will be:
[tex]n-80[/tex]The square of the difference will be:
[tex](n-80)^2[/tex]mr Smith is flying his single engine plane at an altitude of 2400 feet. he sees a cornfield at an angle of depression of 30 degrees. what is his horizontal distance to the corn field?
Let the horizontal distance be represented with x
By Trigonometric Ratio,
[tex]\begin{gathered} \tan 30=\frac{2400}{x} \\ \text{cross multiply, we get,} \\ x=\text{ }\frac{2400}{\tan30}=\text{ 4156.922}\approx\text{ 4156.9 fe}et \end{gathered}[/tex]If m 2 DFC = 40° and m= 55°, then mCDBG2580135
Here we are given a geometrical shape with the following inner and an arc angle as follows:
[tex]The property to note here is from geometric properties of a circle.Property: The inner angle is always the mean of corresponding verticaly opposite arc angles.
We can express the above property in lieu to the geometry question at hand. We see that the two arc angles:
[tex]\text{Arc CD = 55 degrees , Arc BG = ?}[/tex]Ther inner vertically opposite angle are:
[tex]<\text{ DFC < }BFG\text{= 40 degrees }[/tex]The property can be expressed mathematically as follows:
[tex]<\text{ DFC = }\frac{1}{2}\cdot\text{ ( Arc CD + Arc BG )}[/tex]Next plug in the respective values of angles and evaluate for the arc angle BG as follows:
[tex]\begin{gathered} 40\text{ = }\frac{1}{2}\cdot\text{ ( 55 + Arc BG )} \\ 80\text{ = 55 + Arc BG } \\ \text{\textcolor{#FF7968}{Arc BG = 25 degrees}} \end{gathered}[/tex]Therefore the correct option is:
[tex]\textcolor{#FF7968}{25}\text{\textcolor{#FF7968}{ degrees}}[/tex]Using the graph of f(x)=x^2 as a guide describe the transformations and then sketch a graph of each function g(x)=(x-5)^2
1) In comparison to that parent function y =x², in g(x) = (x-5)² we have a horizontal translation to the right. in 5 units.
2) As we can see below:
Note that the Potting tool expands the (x-5)².
by noon the temperature in Buffalo had risen to 18 degrees farenheit what was the temperature there at noon Buffalo is a - 9
If the temperature of buffalo rised 18 degrees means that it is an addition between the 2 temperatures
[tex]-9+18=9[/tex]the temperature at noon is 9°F
450 students are graduating. 68% are going to college. 14% are working. How many students are unsure about what to do?
ANSWER
81 students
EXPLANATION
We have that 450 students are graduating.
68% (out of 100%) are going to college while 14% (out of 100%) are working.
To find the percentage of the studetns that are unsure about what to do, we have to subtract the percentages of those that know what to do from 100%.
That is:
100 - (68 + 14)
=> 100 - 82
=> 18%
Therefore, 18% of people are unsure about what to do.
Now, to find the number of students, we multiply this percent by the total number of students (450):
[tex]\begin{gathered} \frac{18}{100}\cdot450 \\ =\text{ 81} \end{gathered}[/tex]81 students are unsure about what to do.
13.Find the missing side. Round to the nearest tenth.25912XA.5.6B. 7.1С8.1D. 25.7
We were provided with a right-angled triangle. For a right-angled triangle, we can use the trigonometric ratios to solve for unknown sides or angles.
First, let's label the triangle to determine the trigonometric ratios to use:
From the diagram above, we are given:
adjacent = 12
angle = 25 degrees
x = oppossite
We are going to use the tangent ratio, which is:
[tex]\tan \text{ }\phi\text{ = }\frac{opposite}{adjacent}[/tex]When, we substitute the given data, we have:
[tex]\begin{gathered} \tan 25^0\text{ = }\frac{x}{12} \\ x=tan25^0\text{ }\times\text{ 12} \\ =\text{ 5.6 (nearest tenth)} \end{gathered}[/tex]Answer: x = 5.6 (option A)
Evaluate. 3/4 - 1/2 × 7/8 Write your answer in simplest form.
we have the expression
3/4 - 1/2 × 7/8
so
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
First Multiplication
so
[tex]\frac{1}{2}\cdot\frac{7}{8}=\frac{7}{16}[/tex]substitute
[tex]\frac{3}{4}-\frac{7}{16}[/tex]Remember that
3/4 is equivalent to 12/16 (multiply by 4 both numerator and denominator)
substitute
[tex]\frac{12}{16}-\frac{7}{16}=\frac{5}{16}[/tex]therefore
the answer is 5/16I need help to:Determine what the 3 sets of numbers have in common.1. 2/5 and 8/202. 12/28 and 21/493. 10/18 and 15/27
Notice that:
(1)
[tex]\frac{8}{20}=\frac{2\cdot4}{5\cdot4}=\frac{2}{5}\text{.}[/tex]Therefore:
[tex]\frac{8}{20}=\frac{2}{5}\text{.}[/tex](2)
[tex]\begin{gathered} \frac{12}{28}=\frac{3\cdot4}{7\cdot4}=\frac{3}{7}, \\ \frac{21}{49}=\frac{3\cdot7}{7\cdot7}=\frac{3}{7}\text{.} \end{gathered}[/tex]Therefore:
[tex]\frac{12}{28}=\frac{21}{49}\text{.}[/tex](3)
[tex]\begin{gathered} \frac{10}{18}=\frac{5\cdot2}{9\cdot2}=\frac{5}{9}, \\ \frac{15}{27}=\frac{5\cdot3}{9\cdot3}=\frac{5}{9}\text{.} \end{gathered}[/tex]Therefore:
[tex]\frac{10}{18}=\frac{15}{27}\text{.}[/tex]Answer: The 3 sets have in common that in each case both fractions represent the same number.
When broken open Austins jawbreaker will make a hemisphere, what is it surface area if the diameter is 16.4 inches?
When broken open Austen's jawbreaker will make a hemisphere.
Recall that the total surface area of a hemisphere is given by
[tex]TSA=3\pi r^2[/tex]Where r is the radius of the hemisphere.
We are given the diameter of the hemisphere that is 16.4 inches.
The radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{16.4}{2}=8.2\: in[/tex]So, the radius is 8.2 inches
Substitute the radius into the above formula of total surface area
[tex]TSA=3\pi r^2=3\pi(8.2)^2=3\pi(67.24)=633.72\: in^2[/tex]Therefore, the total surface area of the hemisphere is 633.72 square inches.
Please note that if you want to find out only the curved surface area then use the following formula
[tex]CSA=2\pi r^2=2\pi(8.2)^2=453.96\: in^2[/tex]For the given case, the curved surface area is 453.96 square inches.
Study 8 22,29,36 Which expression could be used to find the missing number in the pattern? A. (8 +36) - 2 C. (29-22) + 8 B. (8 x 22) - 2 D. (22 - 7) + 8
8,22,29,36
between 22 - 8 = 14
divide by 2 ,14/2= 7
now add 8+7 = 15
Then anwer is
Option C) (29-22) + 8 = 7 + 8
Find the distance of a wheel where the radius is 10 feet and it gives 15 rotations. How many inches did the wheel travel in those 15 rotations?
We will find the distance after 15 rotations by multiplying the perimeter of the circumference by 15, that is:
[tex]d=15(2\pi r)\Rightarrow d=30\pi(10)\Rightarrow d=300\pi\Rightarrow d\approx941.48[/tex]From this, we have that the wheel traveled approximately 941.48 feet.
The graph below shows the relationship between the amount of time a ferris wheel has been moving and the height above ground of a seat on the ferris wheel. based on the graph. Which statement best describes why height is a function of time in the relationship?
ANSWER
b. Each value of time has exactly 1 value for height associated with it.
EXPLANATION
A function is a relationship where each value of the function has only one value of the variable associated with that value. In this problem, the function is height and the variable is time, therefore the answer is option b.
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. If a random sample of 35 football players is taken, what is the probability that that the random sample will have a mean more than 210 pounds?
We know that
• The mean is 200 pounds.
,• The standard deviation is 25 pounds.
,• The random sample is 35.
First, let's find the Z value using the following formula
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Let's replace the mean, the standard deviation, and x = 210.
[tex]Z=\frac{210-200}{25}=\frac{10}{25}=0.4[/tex]Then, using a p-value table associated with z-scores, we find the probability
[tex]P(x>210)=P(Z>0.4)=0.1554[/tex]Therefore, the probability is 0.1554.The table used is shown below
What is the solution to 4x+6. A x<3 B x<6 C x<48 D x<96
we have the inequality
[tex]4x+6\leq18[/tex]solve for x
subtract 6 both sides
[tex]\begin{gathered} 4x\leq18-6 \\ 4x\leq12 \end{gathered}[/tex]step 2
Divide by 4 both sides
[tex]x\leq3[/tex]19.657 < 19.67 is this true or false
The given expression is
[tex]19.657<19.67[/tex]Notice that the hundredth 7 is greater than 5, this means 19.67 is greater than 19.657.
Therefore, the given expression is false.0.350 km as meters and please show work
Step 1
Given
[tex]0.350\operatorname{km}[/tex]Required; To convert it to meter
Step 2
1 kilometer is equivalent to 1000 meters
Therefore using ratio we will have
[tex]\frac{1\operatorname{km}}{0.350\operatorname{km}}=\frac{1000m}{xm}[/tex]Step 3
Get the conversion to meter
[tex]\begin{gathered} 1\operatorname{km}\text{ }\times\text{ xm = 0.350km }\times\text{ 1000m} \\ \frac{xm\times1\operatorname{km}}{1\operatorname{km}}\text{ = }\frac{\text{ 0.350km }\times\text{ 1000m}}{1\operatorname{km}} \\ xm\text{ = 350 m} \end{gathered}[/tex]Hence, 0.350km as meters = 350m
Mary is 4 years older than Sue. If the sum of their ages is 16. How would you set up the equations?
Answer:
A. x=y-4, x+y=16
C. x=y-4, x+y=16
Explanation:
• Let Sue's age = x
Mary is 4 years older than Sue, therefore:
• Mary's age, y = x+4
[tex]\begin{gathered} y=x+4 \\ \implies x=y-4 \end{gathered}[/tex]Next, the sum of their ages is 16. This gives:
[tex]x+y=16[/tex]Therefore, the equation is:
[tex]\begin{gathered} x=y-4 \\ x+y=16 \end{gathered}[/tex]The correct choices are A and C.
A farmer has 1,416 feet of fencing available to enclose a rectangle area bordering a river. No fencing is required along the river. Let x represent the length of the side of the rectangular enclosure that is perpendicular A(x)= Find the dimensions that will maximize the area. The length of the side rectangle perpendicular to the river is and the length of the side of the rectangle parallel to the river is.What is the maximum area?
The dimensions that will maximize the area are x = 354 ft and y = 708 ft
The length of the side rectangle perpendicular to the river is 354 ft
The length of the side of the rectangle parallel to the river is 708 ft
The maximum area = 250632 ft²
Explanation:Given:
The length of the fencing = 1416 ft
The length of the side rectangle perpendicular to the river = x
To find:
The dimensions that will maximize the area
To determine the dimensions, we will make an illustration of the given information:
let the length o the rectangle parallel to the river = y
Length of the for the enclosed area = Perimeter of the enclosed area
Perimeter of the enclosed area = x + x = y = 2x + y
[tex]1416=2x+y\text{ . . .\lparen1\rparen}[/tex]Area of the rectangle = length × width
length = y, width = x
let the Area of the rectangle = A(x)
[tex]A(x)\text{ = xy . . . \lparen2\rparen}[/tex]To get the expression for A(x), we will make y the subject of the formula in equation (1):
y = 1416 - 2x
substitute for y in equation (2):
[tex]\begin{gathered} A(x)\text{ = x\lparen1416 - 2x\rparen} \\ \\ A(x)\text{ = 14166x - 2x}^2 \end{gathered}[/tex]To get the maximum dimension, we will differentiate with respect to x:
[tex]\begin{gathered} A^{\prime}(x)\text{ = 1416 - 4x} \\ \\ At\text{ maximum, A'\lparen x\rparen = 0:} \\ 1416\text{ - 4x = 0} \\ 1416\text{ = 4x} \\ x\text{ = }\frac{1416}{4} \\ x\text{ = 354} \end{gathered}[/tex]substitute for x in equation (1):
[tex]\begin{gathered} 1416\text{ = 2\lparen354\rparen + y} \\ 1416\text{ - 708 = y} \\ y\text{ = 708} \end{gathered}[/tex]The dimensions that will maximize the area are x = 354 ft and y = 708 ft
The length of the side rectangle perpendicular to the river is 354 ft
The length of the side of the rectangle parallel to the river is 708 ft
The maximum area = 354 × 708
The maximum area = 250632 ft²
The formula is A=P(1+r/n)^nt8. Oswald Chesterfield Cobblepot invests $5,000 into an account that earns 2.5% interestcompounded monthly.a. How much money is in the account after two years? Use the formula above.Answer:b. How much money in interest was earned?Answer:
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given formula with definition of terms
Compounded Amount is gotten using:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]Where:
A =final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
STEP 2: Write the given parameters
[tex]P=5000,r=\frac{2.5}{100}=0.025,t=2,n=12\text{ since it is compounded monthly}[/tex]STEP 3: Calculate the Compounded Amount
[tex]\begin{gathered} A=5000(1+\frac{0.025}{12})^{2\times12} \\ A=5000(1+0.002083333333)^^{24} \\ A=5000\times1.0020833333^{24} \\ A=5000\times1.05121642 \\ A=5256.0821 \\ A\approx5256.08 \end{gathered}[/tex]STEP 4: Calculate the compounded interest
[tex]\begin{gathered} Interest=Amount-Principal \\ \text{By substitution,} \\ Interest=5256.08-5000 \\ Interest=256.08 \end{gathered}[/tex]Hence,
$5256.08 was in the account after 2 years
The interest earned was $256.08
Solve the inequality. Graph the solution.Z/4 is less than or equal to 12.
You have the following inequality:
z/4 ≤ 12
To solve the previous inequality you proceed as follow:
z/4 ≤ 12 multiply both sides by 4
z ≤ 48
Hence, the solution is z ≤ 48
when you want to graph a solution of the form "z lower or equal than", you draw a black point, that means the solution are all number lower than 48, including 48.
Last weekend, 26, 675 tickets were sold at County Stadium. This weekend 24,567 tickets were sold at County Stadium. If you estimate the number of tickets County Stadium sold over the two weekends by rounding each number to the nearest thousand, then you will find there were about ____ tickets sold.
We have the tickets sold each weekend:
• Last weekend: 26,675
,• This weekend: 24,567
We have to find how many tickets where sold in both weekends by rounding each number to the nearest thousand units. This will let us do the math without a calculator.
Then, we can approximate 26,675 to 27,000 and 24,567 to 25,000.
NOTE: we round the numbers up because the next number is 5 or greater. Then 675 is and 567 are approximated as 1,000.
We then can add them as: 27,000+25,000 = 52,000.
Answer: the solution is about 52,000 tickets sold.
NOTE: the exact solution would have been 51,242
question 15:A new webpage received 5,000 page views on the first day. The number of page views decreased by 10% every day. How many total page views did the webpage have after seven days? Round to the nearest whole number.
Explanation
This question wants us to compute the depreciation formula and also get the value of the total page views did the webpage have after seven days.
The general formula is given by
[tex]A=P(1-\frac{r}{100})^n[/tex]In our case
[tex]\begin{gathered} A=? \\ P=5000 \\ r=10 \\ n=n \end{gathered}[/tex]Thus, we will have
[tex]A=5000(1-\frac{10}{100})^n[/tex]We will now have to write the first three terms of the expression to get the required equation
[tex]\begin{gathered} when\text{ n=1} \\ A_1=5000(0.9)^1=4500 \end{gathered}[/tex][tex]\begin{gathered} when\text{ n=2} \\ A_2=5000(0.9)^2=4050 \end{gathered}[/tex]Now, we can list the first three terms as
[tex]5000,4500,4050[/tex]With the above, we can now compute the total web pages after 7 days using the sum of the geometric sequence:
We will get the common ratio
[tex]ratio=r=\frac{4500}{5000}=0.9[/tex][tex]\begin{gathered} S=\frac{a(1-r^n)}{1-r} \\ \\ a=5000 \\ r=0.9 \\ n=7 \end{gathered}[/tex][tex]S=\frac{5000(1-0.9^7)}{1-0.9}=26085[/tex]
Thus, we can see that the answer is option C
[tex]\frac{5000(1-0.9^7)}{1-0.9}=26,085[/tex]Working together, Sarah and Heidi can clean the garage in 2 hours. If they work alone, it takes Heidi 3 hours longer than it takes Sarah. How long would it take Heidi to clean the garage alone?
Given the rates:
[tex]\begin{gathered} \frac{1}{t}=Sarah^{\prime}s\text{ }Rate \\ \\ \frac{1}{t+3}=Heidi^{\prime}s\text{ }Rate \\ \\ \frac{1}{2}=Rate\text{ }working\text{ }together \end{gathered}[/tex]Add their rates of cleaning to get rate working together:
[tex]\frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}[/tex]Solving for t:
[tex]\begin{gathered} \frac{2(t+3)+2t-t(t+3)}{2t(t+3)}=0 \\ \\ \frac{2t+6+2t-t^2-3t}{2t(t+3)}=0 \\ \\ \frac{t+6-t^2}{2t(t+3)}=0 \\ \\ -t^2+t+6=0 \\ \\ (t+2)(t-3)=0 \end{gathered}[/tex]Hence:
t = -2
t = 3
Time can't be negative; then:
Heidi's time: t + 3
3 + 3 = 9
ANSWER
It will take Heidi 9 hrs to clean garage working alone
Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.Interval notation for the above graph in inequality is______
Answer:
[tex](-∞,4)[/tex]Step-by-step explanation:
To solve the following inequality, use inverse operations.
[tex]\begin{gathered} -8x-4>-36 \\ -8x>-32 \\ x<\frac{-32}{-8} \\ x<4 \\ \text{ Interval notation:} \\ (-∞,4) \end{gathered}[/tex]Now, for the number line representing this inequality: