Answers
If a rectangle whose length is 10 centimeter more than its width, then the width of the rectangle is x centimeter and the length of the rectangle is 10+x centimeters
The width of the rectangle = x centimeter
The length is 10 centimeter more than its width
Then the length of the rectangle = 10 + The width of the rectangle
Substitute the value of the width of the rectangle in the equation
The length of the rectangle = 10+x centimeter
Hence, if a rectangle whose length is 10 centimeter more than its width, then the width of the rectangle is x centimeter and the length of the rectangle is 10+x centimeters
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Related Questions
Use the sequence below to complete each task. 3, -15, 75, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 5th term (as) Algebra), 2013 → B I y Default A A : = 5 川里
Answers
a)
This is a geometric sequence, this means that each value of the sequence is multiplied by the common ratio to determine the next number.
For the sequence {3,-15,75}
Divide one of the given numbers by the number before it on the sequence to determine the common ratio
[tex]r=\frac{-15}{3}=-5[/tex]The common ratio for this sequence is r=-5
b)
a is the first value of the sequence
r is the common ratio
k is the place on the sequence of the required value
You can calculate said value using
[tex]ar^k[/tex]c)
For
a=3
r=-5
k=5
The value fo the sequence is
[tex]ar^k=3(-5)^5=-9375[/tex]Identify the percent represented by the 10 × 10 grids
PLEASE ANSWER 28 POINTS
Answers
Answer:
Step-by-step explanation:
10 times 10 means 100 percent
Then identify the second one:
it has three rows of 10 + the 6 more
So: each row is 10 percent:
100+30+6=
136 Percent!
2 1. Determine the missing length in the following triangle. Round to the nearest tenth. (2 points: 1 point for correct answer, 1 point for showing your work) 20 Xe 16 Your answer
Answers
Here, we have a right triangle with a missing side length.
To determine the length of the missing side, apply pythagorean theorem
[tex]c^2=a^2+b^2[/tex]Where:
c is the longest side (hypotenuse) = 20
a = 16
Substitute values into the equation and solve for the missing side.
We have:
[tex]\begin{gathered} 20^2=16^2+x^2 \\ \\ 400=256+x^2 \end{gathered}[/tex]Subtract 256 from both sides:
[tex]\begin{gathered} 400-256=256-256+x^2 \\ \\ 144=x^2 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{144}=\sqrt[]{x^2} \\ \\ 12=x \\ \\ x=12 \end{gathered}[/tex]Therefore, the missing length is 12 units
ANSWER:
x = 12
Purple Dynasty at Smyrna High needs to raise at least $350 to purchase equipment for school beautification. They plan to sell mini pies (x) and bags of candy (y). They will earn $3 profit on each mini pie and $1 profit on each bag of candy. Which could NOT be a way to earn enough money? a) Selling 60 mini pies and 160 bags of candy b) Selling 25 mini pies and 290 bags of candy c) Selling 30 mini pies and 260 bags of candy d) Selling 45 mini pies and 220 bags of candy
Answers
350 = 3x + y
a) 3x + y ==> 3(60) + 160 = 180 + 160 = 340 This is NOT a way to earn enough money
b) 3x + y ==> 3(25) + 290 = 75 + 290 = 365 This IS a way to earn enough money
c) 3x + y ==> 3(30) + 260 = 90 + 260 = 350 This IS a way to earn enough money
d) 3x + y ==> 3(45) + 220 = 135 + 220 = 355 This IS a way to earn enough money
Answer:
Option a
A slide 4.1 meters long makes an angle of 35 degrees with the ground. To the nearest tenth of a meter, how far above the ground is the top of the slide? (image attached)
Answers
Answer:
2.4 meters
Explanation:
In the given right triangle:
• The side length ,opposite ,35° = x
,• The length of the ,hypotenuse ,= 4.1 meters
We want to solve for x.
Using the trigonometric ratios of right triangles:
[tex]\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \implies\sin35\degree=\frac{x}{4.1} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} x=4.1\times\sin35\degree \\ x=2.35 \\ x\approx2.4\text{ meters} \end{gathered}[/tex]The top of the slide is approximately 2.4 meters above the ground.
1) w(n)=n-5; Find w(4)2) g(x)= -[x]: Find g(-4)3) h(n) = 3 | n + 2|; Find h(5)4)h(a) = a^3 + 3a^2; find h(-5)5)p(n)=n^2 - 4n; find p(3)
Answers
1) w(n)=n-5; Find w(4)
2) g(x)= -[x]: Find g(-4)
3) h(n) = 3 | n + 2|; Find h(5)
4)h(a) = a^3 + 3a^2; find h(-5)
5)p(n)=n^2 - 4n; find p(3)
Part 1)
we have
w(n)=n-5
Remember that
w(4) is the value of the function w(n) for n=4
so
substitute the value of n=4 in the equation
w(4)=4-5
w(4)=-1
Part 2
g(x)= -[x]
Find h(5)
For x=5
g(5)=-[5]
g(5)=-5
we have
Part 3
we have
h(n) = 3 | n + 2|
Find h(5)
For n=5
h(5)=3 | 5 + 2|
h(5)=3 | 7|
h(5)=21
Part 4
h(a) = a^3 + 3a^2
Find h(-5)
For a=-5
substitute
h(-5)=(-5)^3+3(-5)^2
h(-5)=-125+75
h(-5)=-50
Part 5
p(n)=n^2 - 4n
Find p(3)
For n=3
substitute
p(3)=3^2-4(3)
p(3)=9-12
p(3)=-3
I need help please answer the following question:
Answers
Answer:
A
Step-by-step explanation:
We have to look at the x axis. The graph starts in x=0 and stops in x=5
Which of the following graphs is described by the function givenbelow?y-2x2+ 6x13Graph BGraph AGraph DGraph C
Answers
Given
[tex]y=2x^2+6x+3[/tex]We want to draw the graph
Solution
Before, I send the graph, Let us get the coordinate of the vertex
From
[tex]undefined[/tex]In how many ways can 7 people line up for play tickets?A. 40,320B. 5,040C. 823,543D. 7
Answers
Given the question: In how many ways can 7 people line up for play tickets?
The number of ways for the first = 7
The number of ways for the second = 6
The number of ways for the third = 5
The number of ways for fourth = 4
The number of ways for the fifth = 3
The number of ways for the sixth = 2
The number of ways for the seventh = 1
So, the total number of ways = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040
So, the answer will be option B. 5,040
When the hands of a clock are on 12 and 4, they form a 120° angle. What angle is formed if the hands are moved to 4 and 6
Answers
The 12 major intervals in a clock form 360°/12 = 30° between each two consecutive numbers.
Therefore, if the hands are moved to 4 and 6, the angle formed must be (6 - 4)*30° = 60°
solve 67 and 68, I leave bad reviews if you leave the session.
Answers
Solution
67)
[tex]\begin{gathered} sec\theta\text{ = }\frac{1}{cos\theta} \\ Cross\text{ multiply} \\ sec\theta\text{ }\times\text{ cos}\theta \\ \frac{1}{cos\theta}\text{ }\times cos\theta \\ =\text{ 1} \end{gathered}[/tex]68)
Draw a right angle triangle:
[tex]\begin{gathered} sin\theta\text{ = }\frac{opposite}{hypotenuse}\text{ = }\frac{a}{c} \\ cos\theta\text{ = }\frac{adjacent\text{ }}{Hypotenuse}\text{ = }\frac{b}{c} \\ tan\theta\text{ = }\frac{opposite}{adjacent\text{ }}\text{ = }\frac{a}{b} \end{gathered}[/tex][tex]\begin{gathered} \\ \frac{sin\theta\begin{equation*}\end{equation*}}{cos\theta}\text{ = }\frac{a}{c}\text{ }\div\text{ }\frac{b}{c} \\ =\text{ }\frac{a}{c}\text{ }\times\text{ }\frac{c}{b} \\ =\text{ }\frac{a}{b} \\ Hence,tan\theta\text{= }\frac{sin\theta}{cos\theta} \end{gathered}[/tex]I need help with this practiceThe subject is complex numbers and vectors*It asks to fill in the four boxes, *enter the roots in order of increasing angle measure
Answers
ANSWER:
[tex]\begin{gathered} \:\sqrt[4]{4}cis\left(-\frac{\pi }{24}\right)\: \\ \\ \:\sqrt[4]{4}cis\left(\frac{11\pi}{24}\right)\: \\ \\ \:\sqrt[4]{4}cis\left(\frac{23\pi}{24}\right)\: \\ \\ \:\sqrt[4]{4}cis\left(\frac{35\pi}{24}\right)\: \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]2\sqrt{3}-2i[/tex]To calculate the 4 roots we must match the equation with x raised to 4, just like this:
[tex]x^4=2\sqrt{3}-2i[/tex]For this case the roots are given as follows:
[tex]\begin{gathered} \:z_k=\sqrt[n]{\left|a\right|}\left(\cos\left(\frac{\arctan\left(\alpha\right)+2k\pi}{n}\right)+i\sin\left(\frac{\arctan\left(\alpha\right)+2k\pi}{n}\right)\right) \\ \\ \text{ In this case:} \\ \\ n=4 \\ \\ |a|=\sqrt{\left(2\sqrt{3}\right)^2+\left(-2\right)^2}=\sqrt{12+4}=\sqrt{16} \\ \\ a=4 \\ \\ \alpha=\left(\frac{-2}{2\sqrt{3}}\right) \\ \\ \text{ Therefore:} \\ \\ \arctan\left(\frac{-2}{2\sqrt{3}}\right)=-\frac{\pi}{6} \end{gathered}[/tex]Taking into account the above, we calculate for each x,
when k = 0,1, 2 3, just like this:
[tex]\begin{gathered} x_1=\sqrt[4]{4}\left(\cos\left(\frac{-\frac{\pi}{6}+2\cdot\:0\pi}{4}\right)+i\sin\left(\frac{-\frac{\pi}{6}+2\cdot\:0\pi}{4}\right)\right)=\sqrt[4]{4}\left(\cos\left(-\frac{\pi}{24}\frac{}{}\right)+i\sin\left(-\frac{\pi}{24}\right)\right)=\sqrt[4]{4}cis\left(-\frac{\pi}{24}\right) \\ \\ x_2=\sqrt[4]{4}\left(\cos\left(\frac{-\frac{\pi}{6}+2\cdot\:1\pi}{4}\right)+i\sin\left(\frac{-\frac{\pi}{6}+2\cdot\:1\pi}{4}\right)\right)=\sqrt[4]{4}\left(\cos\left(\frac{11\pi\:}{24}\right)+i\sin\left(\frac{11\pi\:}{24}\right)\right)=\:\sqrt[4]{4}cis\left(\frac{11\pi\:}{24}\right)\: \\ \\ x_3=\sqrt[4]{4}\left(\cos\left(\frac{-\frac{\pi}{6}+2\cdot\:2\pi}{4}\right)+i\sin\left(\frac{-\frac{\pi}{6}+2\cdot\:2\pi}{4}\right)\right)=\sqrt[4]{4}\left(\cos\left(\frac{23\pi\:}{24}\right)+i\sin\left(\frac{23\pi\:}{24}\right)\right)=\sqrt[4]{4}cis\left(\frac{23\pi\:}{24}\right)\: \\ \\ x_4=\sqrt[4]{4}\left(\cos\left(\frac{-\frac{\pi}{6}+2\cdot\:3\pi}{4}\right)+i\sin\left(\frac{-\frac{\pi}{6}+2\cdot\:3\pi}{4}\right)\right)=\sqrt[4]{4}\left(\cos\left(\frac{35\pi\:}{24}\right)+i\sin\left(\frac{35\pi\:}{24}\right)\right)=\:\sqrt[4]{4}cis\left(\frac{35\pi\:}{24}\right)\: \end{gathered}[/tex]5. An equation that crosses the y-axis at -5 and crosses the point (2,3)
Answers
For a straight line graph, the point at which the line crosses the y axis is called the y intercept. From the information given, the line crosses the y axis at - 5. This means that the y intercept is - 5
We would write the equation in the slope intercept form whicg is expressed as
y = mx + c
Where m represents the slpoe
We would substitute x = 2, y = 3 and c = - 5 in the equation above to determine the slope, m. It becomes
3 = m * 2 - 5
3 = 2m - 5
3 + 5 = 2m
2m = 8
m = 8/2
m = 4
The equation would be
y = 4x - 5y interceptF
A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze, and the second brand is 70% pure antifreeze. In order to obtain 60 gallons of a mixture that contains 40% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answers
Given:
The first brand is 30% anti-freeze
The second brand is 70% anti-freeze.
We want to make a 60 gallons mixture that has 40% anti-freeze.
Solution
Let the gallons of the first brand be x
Hence the gallons of the second brand would be:
[tex]=60\text{ - x}[/tex]The gallons of the first brand that would be pure anti-freeze:
[tex]\begin{gathered} =\text{ }\frac{30}{100}\text{ }\times\text{ x} \\ =\text{ 0.3x} \end{gathered}[/tex]The gallons of the second brand that would be pure anti-freeze:
[tex]\begin{gathered} =\text{ }\frac{70}{100}\text{ }\times\text{ (60-x)} \\ =\text{ 0.7(60-x)} \end{gathered}[/tex]The gallons of the mixture that would be pure anti-freeze:
[tex]\begin{gathered} =\text{ }\frac{40}{100}\text{ }\times\text{ 60} \\ =\text{ 0.4 }\times\text{ 60} \\ =\text{ 24} \end{gathered}[/tex]On mixing, we have the equation:
[tex]0.3x\text{ + 0.7(60-x) = 24}[/tex]When we solve for x, we have:
[tex]\begin{gathered} 0.3x\text{ + 42 -0.7x = 24} \\ \text{Collect like terms} \\ 0.3x\text{ - 0.7x = 24 -42} \\ -0.4x\text{ = -18} \\ \text{Divide both sides by -0.4} \\ \frac{-0.4x}{-0.4}\text{ =}\frac{-18}{-0.4} \\ x\text{ = 45} \end{gathered}[/tex]Hence, the gallons of the first brand required to obtain a mixture of 40% anti-freeze is 45 gallons.
The gallons of the second brand required would be:
[tex]\begin{gathered} =60\text{ - 45} \\ =\text{ 15 gallons} \end{gathered}[/tex]Answer:
First brand = 45 gallons
Second brand = 15 gallons
On a sunny day, a flag pole and its shadow form the sides of a right triangle, if the hypotenuse is 52 meters long and the shadow is 48 meters. How tall is the flag pole?
Answers
The right triangle formed by the flagpole and its shadow is shown below
From the right triangle,
BC represents the height of the flagpole
AC is the hypotenuse of the triangle
AB is the length of the shadow
To find BC, we would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
one leg = BC
other leg = 48
By applying the theorem, we have
52^2 = 48^2 + BC^2
2704 = 2304 + BC^2
Subtracting 2304 from both sides of the equation, we have
2704 - 2304 = 2304 - 2304 + BC^2
BC^2 = 400
BC = square root of 400
BC = 20
Option D is correct
find the functions and simplify
Answers
Given the functions f(x) and g(x), as follows:
[tex]f(x)=\frac{1}{x-4}[/tex]and
[tex]g(x)=\frac{5}{x}+4[/tex]Now:
(a) f(g(x)) is obtained as follows:
[tex]\begin{gathered} f(x)=\frac{1}{x-4}\text{ and }g(x)=\frac{5}{x}+4 \\ \Rightarrow f(g(x))=\frac{1}{(\frac{5}{x}+4)-4}\text{ } \\ \Rightarrow f(g(x))=\frac{1}{\frac{5}{x}}=\frac{x}{5} \\ \Rightarrow f(g(x))=\frac{x}{5} \end{gathered}[/tex](b) g(f(x)) is obtained as follows:
[tex]\begin{gathered} f(x)=\frac{1}{x-4}\text{ and }g(x)=\frac{5}{x}+4 \\ \Rightarrow g(f(x))=\frac{5}{\frac{1}{x-4}}+4=5(x-4)+4 \\ \Rightarrow g(f(x))=5(x-4)+4=5x-20+4=5x-16 \\ \Rightarrow g(f(x))=5x-16 \end{gathered}[/tex]Work out the surface area of this solid prism. 25cm 17cm 15cm 30cm 28cm The diagram is not drawn to scale. cm2
Answers
To calculate we have to break down the shape into the respective surfaces
The area of a triangle is
[tex]\begin{gathered} \text{Area}=\frac{1}{2}\times base\times height \\ \text{where,} \\ \text{base}=28\operatorname{cm} \\ \text{height}=15\operatorname{cm} \end{gathered}[/tex]Substituting the values, we will have
[tex]\begin{gathered} \text{Area}=\frac{1}{2}\times28\operatorname{cm}\times15\operatorname{cm} \\ \text{Area}=14\times15 \\ \text{Area}=210\operatorname{cm}^2 \end{gathered}[/tex]Secondly, we will bring out the base
The area of a rectangle is
[tex]\begin{gathered} \text{Area}=\text{Length}\times breadth \\ \text{where,} \\ \text{length}=30\operatorname{cm} \\ \text{breadth}=28\operatorname{cm} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Area}=\text{Length}\times breadth \\ \text{Area}=30\operatorname{cm}\times28\operatorname{cm} \\ \text{Area}=840\operatorname{cm}^2 \end{gathered}[/tex]Thirdly,
We will bring the out slant rectangular faces
The area of a rectangle is
[tex]\begin{gathered} \text{Area}=\text{Length}\times breadth \\ \text{where,} \\ \text{length}=30\operatorname{cm} \\ \text{breadth}=25\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} \text{Area}=30\operatorname{cm}\times25\operatorname{cm} \\ \text{Area}=750\operatorname{cm}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the second slant rectangular face=Length}\times breadth \\ \text{Area of the second slant rectangular face}=17\operatorname{cm}\times30\operatorname{cm}= \\ \text{Area of the second slant rectangular face}=510\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The total surface area of the solid prism will be
[tex]\begin{gathered} \text{Total}=\text{ (area of two triagular faces) + (area of the base) + (area of the rectangular slant faces)} \\ \text{Total surface area = }(2\times210cm^2)+(840\operatorname{cm})+(750\operatorname{cm})+(510\operatorname{cm}) \\ \text{Total surface area}=420\operatorname{cm}+840\operatorname{cm}+750\operatorname{cm}+510\operatorname{cm} \\ \text{Total surface area}=2,520\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The final answer is = 2,520cm²
Express (4x3 + 5x + 1)/(x2 + 1) using long division method in the form q(x) + r(x)/b(x) where q(x) is the quotient, r(x) is the remainder, and b(x) is the divisor.
Answers
Answer:
4x + (x + 1) / (x^2 + 1)
Explanation:
We perform the long division
The result of the above long division tells is that
[tex]4x^3+5x+1=4x(x^2+1)+(x+1)[/tex]If we now divide both sides by x^2 + 1, we get
[tex]\frac{4x^3+5x+1}{x^2+1}=\frac{4x(x^2+1)+(x+1)}{x^2+1}[/tex][tex]=\frac{4x(x^2+1)}{x^2+1}+\frac{(x+1)}{x^2+1}[/tex][tex]=4x+\frac{x+1}{x^2+1}[/tex]Hence,
[tex]\boxed{\frac{4x^3+5x+1}{x^2+1}=4x+\frac{x+1}{x^2+1}\text{.}}[/tex]Therefore, the first choice from the options is the correct answer!
4. The area of the base of the regular quadratic pyramid SABCD is 25 cm2 and the area of the side wall SAB is 15 cm2. Calculate: 1) the length of the base edge; 2) the length of the diagonal of the base; 3) the length of the apothem; 4) the length of the side edge;
Answers
Answer:
1) 5 cm
2) 7.07 cm
3) 6 cm
4) 6.5 cm
Step-by-step explanation:
Part 1:
Since we're looking at a square pyramid, we'll have that the area of the base is the area of a square:
[tex]A_b=L^2[/tex]Since we know this area is 25 square centimiters, we can find L as following:
[tex]\begin{gathered} 25=L^2 \\ \rightarrow L=\sqrt{25} \\ \\ \Rightarrow L=5 \end{gathered}[/tex]Therefore, we can conlcude that the length of the base edge is 5 cm
Part 2:
The lenght of the diagonal of a square is given by the formula:
[tex]D=\sqrt{2}\text{ }L[/tex]Where L is the lenght of the sides of the square. Since we've already calculated this lenght, we can find the lenght of the diagonal as following:
[tex]\begin{gathered} D=(\sqrt{2})(5) \\ \\ \Rightarrow D=7.07 \end{gathered}[/tex]This way, we can conclude that the length of the diagonal of the base is 7.07 cm
Part 3:
Let's take a look at a drawing of side wall SAB:
Remember that the formula used to calculate the area of a triangle is:
[tex]A_t=\frac{bh}{2}[/tex]Where:
• b, is the base of the trianlge
,• h, is the height of the triangle. In this case, the apothem ,(a)
Since we already know this area, we can find a as following:
[tex]\begin{gathered} 15=\frac{5\times a}{2}\rightarrow30=5a\rightarrow\frac{30}{5}=a \\ \\ \Rightarrow a=6 \end{gathered}[/tex]This way, we can conlcude that the length of the apothem is 6 cm
Part 4:
Now we know the apothem, let's take another look at side wall SAB:
We can extract from here the following right triangle:
Using the pythagorean theorem, we'll have that :
[tex]l^2=2.5^2+6^2[/tex]Solving for l,
[tex]\begin{gathered} l=\sqrt{2.5^2+6^2} \\ \\ \Rightarrow l=6.5 \end{gathered}[/tex]Therefore, we can conlcude that the length of the side edge is 6.5 cm
if it rains 12 1/4 inches of rain in 25 1/2 hours .What is the approximate rainfall rate in inches per hour
Answers
Let:
y = Amount of rain
x = Time
The rainfall rate is given by:
[tex]rain_{}fall_{\text{ }}rate=\frac{Amount_{\text{ }}of_{\text{ }}rain}{Time}[/tex]Let's convert the mixed numbers into fractions:
[tex]12\frac{1}{4}=\frac{12\cdot4+1}{4}=\frac{48+1}{4}=\frac{49}{4}=12.25[/tex][tex]25\frac{1}{2}=\frac{25\cdot2+1}{2}=\frac{50+1}{2}=\frac{51}{2}=25.5[/tex]Therefore:
[tex]rain_{}fall_{\text{ }}rate=\frac{12.25}{25.5}\approx0.48[/tex]I need help with 14 and 18 please step by step
Answers
14) Notice that:
[tex]136.5=13.65\times10.[/tex]Therefore:
[tex]136.5\div10=(13.65\times10)\div10.[/tex]Now, we know that:
[tex](a\times b)\div b=a\text{.}[/tex]Then:
[tex](13.65\times10)\div10=13.65.[/tex]18) Notice that:
[tex]8100=0.81\times10^4\text{.}[/tex]Therefore:
[tex]\begin{gathered} 8100\div10^4=(0.81\times10^4)\div10^4 \\ =0.81. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} 136.5\div10=13.65, \\ 8100\div10^4=0.81. \end{gathered}[/tex]Answer:
(Q.14) 13.65
(Q.18) .81
Step-by-step explanation:
(Q.14)
136.5/10
1365/10 * 1/10
1365/100
13.65
(Q.18)
8100/10000
8100*1/10000
81/100
.81
Out of 310 racers who started the marathon, 277 completed the race, 21 gave up, and 12 weredisqualified. What percentage did not complete the marathon?
Answers
From the question we have the following information given;
[tex]\begin{gathered} \text{Total racers}=310 \\ \text{Completed}=277 \\ \text{Gave up}=21 \\ \text{Disqualified}=12 \end{gathered}[/tex]This means the number of racers that did not complete the marathon was a total of those who gave up and those who were disqualified. That is, 33 racers did not complete the marathon.
Therefore, the percentage that did not complete the marathon would be calculated as follows;
[tex]\begin{gathered} Did\text{ not complete}=\frac{33}{310}\times100 \\ \text{Did not complete}=\frac{3300}{310} \\ \text{Did not complete}=10.645\% \\ \text{Rounded to the nearest hundredth;} \\ \text{Did not complete}=10.65\% \end{gathered}[/tex]ANSWER:
The percentage that did not complete the marathon was 10.65%
A salesperson at a jewelry store earns 4% commission each week. Last week, Heidi sold $710 worth of jewelry. How much did the jewelry store make from her sales? Heidi earned $ 28.40 in commission. The store made $ from her sales.
Answers
The store made the difference between $710 and $28.40, so:
[tex]\text{store}=710-28.40=681.60[/tex]The store made $681.60.
Find the probability that if you threw a dart randomly in the large rectangle below that itwould land in the square.35二+20f
Answers
Assuming the randomly throw is equally distributed along the rectangle area, the probability of hitting the square is the fraction of the area of the square with respect to the total are of the rectangle.
The area of the square is the square of its side:
[tex]A_{square}=3^2=9[/tex]And the area of the rectangle is the product of its lengths by its height:
[tex]A_{rectangle}=5\cdot20=100[/tex]So, the probability is the area of the square divided by the area of the rectangle:
[tex]P=\frac{9}{100}=0.09=9\%[/tex]The probability if 9%.
An 80% confidence interval for a proportion is found to be (0.27, 0.33). What is the sample proportion?
Answers
Solution
For this case the confidence interval is given by:
(0.27; 0.33)
We can find the estimaed proportion in the following way:
[tex]p=\frac{0.27+0.33}{2}=0.30[/tex]then the sample proportion would be 0.30
If the customer wanted the original 3x5 photo to be twice the size, what would be the new size of the photo?
Answers
If the original photo to be twice the size , then the new size of the photo is 6 x 10 .
In the question ,
it is given that ,
the dimensions of the original photo is 3x5 .
we have to make the photo size twice as original size ,
So , to make the size twice , we multiply the original dimensions of the photo by 2 .
which means ,
the new size = 2*(3x5)
= 2*3 x 2*5
= 6 x 10
hence , the new size is 6x10 .
Therefore , If the original photo to be twice the size , then the new size of the photo is 6 x 10 .
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3% of 17 dollars is what
Answers
Answer
3% 0f $17 is $0.51
Step-by-step explanation:
3% of $17
3% means 3 / 100
Hence, 3/100 x $17
0.03x 17 = $0.51
Henc, 3% 0f $17 is $0.51
For each expression, write an equivalent expression in expanded form.
Answers
Note that:
A(B + C) = AB + AC (Rule of distributivity)
For the given expressions:
-3(2x - 4) = -3(2x) -3(-4)
-3(2x - 4) = -6x + 12
0.1(-90 + 50a) = -0.1(90) + 0.1(50a)
0.1(-90 + 50a) = -9 + 5a
-7(9 - x) = -7(9) -7(-x)
-7(9 - x) = -63 + 7x
A. Write an expression for the volume of a pyramid with base area B and height H. B. Use your expression from part (a) to find the volume of a pyramid with base area of 34 square units and a height of 9 units.
Answers
The expression is given for the volume of pyramid with base B and height H.
In b part, the base area is given 34 sq.units and height is 9 units.w
ExplanationA. To determine the volume of a pyramid with base area B and height H.
The volume of pyramid is
[tex]V=\frac{1}{3}\times B\times H[/tex]B. The area is given 34 square units and a height is 9 units.
To determine the volume of pyramid,
[tex]V=\frac{1}{3}\times B\times H[/tex]Substitute the values B and H and find volume.
[tex]\begin{gathered} V=\frac{1}{3}\times34\times9 \\ V=102cubic\text{ units} \end{gathered}[/tex]AnswerA. The expression for volume of pyramid is
[tex]V=\frac{1}{3}\times B\times H[/tex]B. The volume of pyramid is determined as
[tex]102cubicunits[/tex]Paula wants to use a straightedge and compass to construct segment PS, which is congruent to segment RT in the figure below.
Answers
The length of construct segment PS will be the same as segment RT thus Paula needs to place her compass the distance from R to T so option (D) is correct.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
In other meaning, if you can copy a figure then that copy and the original figure will be congruent.
As per the given,
Paula wants to use a straightedge and compass to construct segment PS.
Given that PS is equal to segment RT.
PS = RT
Therefore,
The width that Paula needs to set is the distance from R to T.
Hence "The length of construct segment PS will be the same as segment RT thus Paula needs to place her compass the distance from R to T".
To learn more about congruence,
https://brainly.com/question/12413243
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