we have
four subtracted from the product of 10 and a number is at most-20
Let
n ----> the number
so
[tex]10n-4\leq-20[/tex]solve for n
[tex]\begin{gathered} 10n\leq-20+4 \\ 10n\leq-16 \\ n\leq-1.6 \end{gathered}[/tex]the solution for n is the interval (-infinite, -1.6]
All real numbers less than or equal to negative 1.6
Timothy ran a lemonade stand for 6 days. on the first day he made $5. Each day after that he made $2 more than the previous day. How much money did Marcus make, , after the 6 days?A) $60B) $15C) $12D) $30
Step `1;
Total number of days = 6
Step 2:
First day = $5
Second day = $5 + $2 = $7
Third day = $7 + $2 = $9
Fourth day + $9 + $2 = $11
Fifth day = $11 + $2 = $13
Sixth day = $13 + $2 = $15
Step 3:
Marcus made = $5 + $7 + $9 + $11 + $13 + $15
= $60
Second method
Use the sum of nth terms of arithmetic progression.
first term a = $5
Common difference = 2
n = 6
[tex]\begin{gathered} S\text{um of the 6 terms = }\frac{n}{2}(\text{ 2a + (n-1)d)} \\ =\text{ }\frac{6}{2}\text{ ( 2}\times5\text{ + (6 -1) }\times\text{ 2)} \\ =\text{ 3( 10 + 5}\times2\text{ )} \\ =\text{ 3( 10 + 10 )} \\ =\text{ 3 }\times\text{ 20} \\ =\text{ \$60} \end{gathered}[/tex]Final answer
Marcus made = $60 Option A
A faraway planet is populated by creatures called Jolos. All Jolos are either green or purple and either one-headed or two-headed. Balan, who lives on this planet, does a survey and finds that her colony of 500 contains 100 green, one-headed Jolos; 125 purple, two-headed Jolos; and 270 one headed-jolos.How many green Jolos are there in Balan's colony?A. 105B. 170C. 205D. 230
According to the table, there are 270 one-headed in total, and there are 500 Jolos, we just have to subtract to find the total of two-headed Jolos
[tex]500-270=230[/tex]There are 230 two-headed Jolos.
Now, we subtract the total of two-headed Jolos and the two-headed purple Jolos to find the total green.
[tex]230-125=105[/tex]There are 105 two-headed green Jolos.
At last, we have to sum the number of one-headed green Jolos and the two-headed green Jolos,
[tex]100+105=205[/tex]Hence, there are 205 green Jolos in total.Write the equation of each line in slope intercept form (see attached)
As we can see we have a horizontal line, the slope of the horizontal line is zero
the form of the equation of the line in slop-intercept form is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
In our case m=0
[tex]\begin{gathered} y=(0)x+b \\ y=b \end{gathered}[/tex]in this case the y-intercept is b=-4
Therefore the equation is
[tex]y=-4[/tex]ANSWER
y=-4
Please help solve thank you
a) 2711/7576
b) 43
=================================================
Explanation:
a) 2711 are e-bikes and there are 3277+2711+1588 = 7576 total bikes. Divide the values to get 2711/7576 . This fraction cannot be reduced because the GCF of 2711 and 7576 is 1.
---------
b) There are 3277 bikes with fat tires out of 7576 total. Use a calculator to get 3277/7576 = 0.43255 approximately. This converts to 43.255% and then rounds to 43%
The percent sign is already typed in, so you just need to type in the whole number 43 for this box.
How4 x 8 sheet ofmanyply wood do you need tocover a 24 x 24 deck?
Given
Dimensions of deck = 24 by 24
dimensions of ply wood = 4 by 8
Find
Number of sheets of ply wood needed to cover the deck
Explanation
number of sheets = area of deck divided by area of 1 ply wood
so ,
area of deck =
[tex]\begin{gathered} 24\times24 \\ 576 \end{gathered}[/tex]and
area of ply wood =
[tex]\begin{gathered} 4\times8 \\ 32 \end{gathered}[/tex]so ,
number of sheets needed =
[tex]\begin{gathered} \frac{576}{32} \\ \\ 18 \end{gathered}[/tex]Final Answer
Hence , the required number of sheets of ply wood is 18
Evaluate (3√2-1) (3√2+1)
Answer:
9√3 converted is 15.58845727
I need help answering the 2nd part of this question
An identity function has one output value for each input value.
G is an identity function.
To find its equation apply the slope-intercept form:
y=mx +b
Where:
m= slope ( rise / run)
b= y-intercept ( where the function crosses the y axis)
By looking at the graph we can see that it crosses (0,0) so, b= 0.
And for every unit to right along the x-axis, it goes up by 1 unit along the y axis.
So, m= 1/1 = 1
Equation:
y = x
1/b + 1/9 + = 1/tSolve for t
The given expression is
[tex]\frac{1}{b}+\frac{1}{9}=\frac{1}{t}[/tex]First, we multiply the equation by t
[tex]\begin{gathered} (\frac{1}{b}+\frac{1}{9})\cdot t=\frac{1}{t}\cdot t \\ (\frac{1}{b}+\frac{1}{9})\cdot t=1 \end{gathered}[/tex]Now, we divide the equation by 1/b + 1/9
[tex]\begin{gathered} \frac{(\frac{1}{b}+\frac{1}{9})\cdot t}{(\frac{1}{b}+\frac{1}{9})}=\frac{1}{(\frac{1}{b}+\frac{1}{9})} \\ t=\frac{1}{(\frac{1}{b}+\frac{1}{9})} \end{gathered}[/tex]Now, we sum fractions
[tex]t=\frac{1}{\frac{9+b}{9b}}[/tex]Then, we solve this combined fraction
[tex]t=\frac{9b\cdot1}{9+b}=\frac{9b}{9+b}[/tex]Therefore, the final expression is
[tex]t=\frac{9b}{9+b}[/tex]Julie has a total of 16 chickens. If she has 4 times as many chickens as dogs, write and solve an equation to determine the number of dogs she has.
The equation that can be used to determine the number of dogs that Julie has =
4× (number of chicken) = 64
What is an equation?An equation is defined as the expression that shows a connection between two variables that are connected with an 'equal to' sign.
The number of chicken owned by Julie = 16 chickens
The number of dogs = X
But she has 4× (number of chicken) = X
That is 4 × 16 = X
X= 64
Therefore the number of dogs that Julie has = 64 dogs.
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The Editor-in-Chief of the student newspaper was doing a final review of the articles submitted for the upcoming edition. Of the 12 total articles submitted, 5 were editorials. If he liked all the articles equally, and randomly selected 5 articles to go on the front cover, what is the probability that exactly 3 of the chosen articles are editorials? Write your answer as a decimal rounded to four decimal places.
This is a problem of binomial probability. We have two possible outcomes:
• the article selected is an editorial,
,• the article selected is not an editorial.
The probability of success (select an article that is an editorial) is:
[tex]p=\frac{5}{12}[/tex]Because we have 12 total articles submitted, and 5 of them were editorials.
To calculate the probability that selecting 5 random articles, getting as a result that exactly 3 of the chosen articles are editorials, we use the binomial probability formula:
[tex]P(n,x)=C(n,x)\cdot p^x\cdot(1-p)^{n-x}[/tex]Where:
• n = the number of trials = the number of articles selected randomly = 5,
,• x = the number of success = the number of editorials that we expect = 3,
,• p = the probability of getting an editorial = 5/12,
,• C(n,x) = n! / (x! (n-x)!).
Replacing the data in the formula above, we get:
[tex]P(n=5,x=3)=\frac{5!}{3!\cdot(5-3)!}\cdot(\frac{5}{12})^3\cdot(1-\frac{5}{12})^{5-3}\cong0.24615=0.2462[/tex]Answer
Rounded to four decimal places, the probability that exactly 3 of the chosen articles are editorials is 0.2462.
7. Martha baked 332 muffins. She packed them in boxes of twelve muffins and sold each full box for S6How much money did she make?
• Given that Martha baked 332 muffins,
,• 332 / 12 = 27.67 boxes
,• If she sold each box for $ 6 ; it will be
27*6 = $162
0.67 * 6 = 4.02
Total 162+4.02 = 166.02≈ $166
• She will make $166, ,
Fiona was playing a game in which she rolled two number cubes. Cube #1 had the integers 1, 2, 3, 4, 5 and 6 on its faces. Cube # 2 has the integers –1, – 2, – 3, –4, –5 and –6 on its faces. She rolled Cube # 1 and got a 2. After she rolled Cube # 2 the sum of the value on the cubes was 0. What number did she roll on Cube # 2?
When Fiona rolled Cube #2, she got a number -2 as she got 2 while rolling Cube #1 and the sum of the value on the cubes was 0.
As we know Cube #1 has integers 1, 2, 3, 4, 5, 6 on its faces and Cube #2 has -1, -2, -3, -4, -5, -6 on its faces.
It is also given that Fiona got 2 when she rolled cube #1 and the value of the sum on both the cubes is 0.
So it is clear that on Cube #2, the number must be -2 as in that case only, the sum of the values will be 0.
To prove
2 + (-1) = 1
2 + (-2) = 0
2 + (-3) = -1
Hence, the number she got on Cube #2 is -2.
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The Connecticut River flows at a rate of 6 km / hour for the length of a popular scenic route. If a cruiser to travels 3 hours with the current to reach a drop-off point, but the return trip against the same current took 7 hours. Find the speed of the boat without a current?The speed of the boat without a current is ____ km/hour. (if needed, round to 2 decimal places).
Given:
Speed of current (y)= 6 km/hour
Distance = d km
Speed of boat in still water = x km/hour
Speed of the cruiser with the current= (x+6) km/hour
Speed of the cruiser against the current= (x-6) km/hour
[tex]\text{Time to travel with the stream=}\frac{d}{x+6}[/tex][tex]3=\frac{d}{x+6}[/tex][tex]3\mleft(x+6\mright)=d[/tex][tex]d=3x+18\ldots.\text{ (1)}[/tex][tex]\text{Time to travel }against\text{ the stream=}\frac{d}{x-6}[/tex][tex]7=\frac{d}{x-6}[/tex][tex]d=7x-42\ldots.\text{ (2)}[/tex]From equation (1) and (2)
[tex]7x-42=3x+18[/tex][tex]7x-3x=18+42[/tex][tex]4x=60[/tex][tex]x=15[/tex]Therefore the speed of the without a current is 15km/hour.
Im confused on how to make the table and plug the dots while also describing both behaviors on this equation.
Here, we want to complete the table
To do this, we consider points on the plot
From what we have;
We are told that a graph of an exponential function does not cross the x-axis and thus, y cannot be zero
When x =0, y = 1
When x = 1, y = 2
when x = 2, y = 4
The y-intercept is the value of y when x = 0; it is the point at which the graph crosses the y-axis
What we have here is that wehn x = 0, y = 1
Hence, 1 is the y-intercept
Now, let us take a look at the end behavior
We can obtain this from the graph;
As x moves towards infinity, the y value moves towards infinity too as evident from the upward curve of the graph
As x moves toward negative infinity, y moves closer to zero
Find the volume of the figure round to the nearest 10th if needed
Given: A triangular prism with base 6ft,height of triangle is 8 ft and height of prism is 12ft
Find : the volume of the prism.
Explanation: the volume of the triangular prism is equal to area of the base triangle times height of the prism.
[tex]\begin{gathered} =\frac{(8\times6)\times12}{2} \\ =288\text{ ft}^3 \end{gathered}[/tex]final answer: the volume of the rectangular prism is
[tex]288ft^3[/tex]The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. If a weight of 8lb stretches a certain spring 9in., how far will the spring stretch if the weight is increased to 37lb? (Leave the variation constant in fraction form. Round off your final answer to the nearest in.)
ANSWER
L = 42in
EXPLANATION
As people are living longer and the world's population is increasing, there are more and more people ages 65 or older. In 2000, approximately 419 million people were 65 or older. By 2017, that number increased to 656 million. On the two questions below, round to the nearest tenth when relevant a. What was the absolute change in the number of people 65 or older from 2000 to 2017? b. What was the relative change in the number of people 65 or older from 2000 to 2017?
In 2000 there were 419 million people 65 or older
In 2017 there were 656 million people 65 or older
a)
To calculate the absolute change in the number of people 65 and older you have to subtract the initial number (on year 2000) from the final number (in year 2017)
[tex]656000000-419000000=240000000[/tex]The absolute change is 240millions
b)
The relative change is the percentage of change. To calculate it you have to calculate the difference between the final number and the initial number, divide the result by the initial number and multiply it by 100
[tex]\frac{240000000}{419000000}\cdot100=57.279\cong57.30[/tex]The relative change is 57.30%
This is due tomorrow! Smart people help me, please!!
The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 433 ft long and 4 mm in diameter has a resistance of 1.22 ohms, find the length of a wire of the same material whose resistance is 1.43 ohms and whose diameter is 5 mm.
Given:
The resistance
im confused on what 43/25 as a percent would be
1------------------------------------>100%
43/25----------------------------->x%
So, using cross multiplication:
[tex]\begin{gathered} \frac{1}{\frac{43}{25}}=\frac{100}{x} \\ \text{solve for x:} \\ x=100\times(\frac{43}{25}) \\ x=172 \end{gathered}[/tex]Please help I need by today only questions 5 and 6 need to show work
Part a: Pot the points X, Y and Z are obtained on graph.
Part b: Distances; XY = 3, YZ = 5 and XZ = √34 units.
Part c: Measure of angles; X = 59.04 degrees and Z = 30.96 degrees.
What is termed as the Pythagorean theorem?The Pythagorean theorem states that the sum of a squares just on legs of a right triangle equals the square just on hypotenuse.For the given question, Triangle XYZ with the vertexes are given.
Part a: Pot the points.
X = (6, 6)
Y = (6, 3)
Z = (1, 3)
The points on the graph are plotted.
Part b: Distances;
XY = 6 - 3 = 3 units
YZ = 6 - 1 = 5 units
XZ , use Pythagorean theorem.
XZ² = XY² + YZ²
Put the values.
XZ² = 3² + 5²
XZ² = 9 + 25
XZ² = 34
XZ = √34 units.
Part c: Measure of angles.
In right triangle XYZ
cos X = XY/XZ
cos X = 3/ √34
X = 59.04 degrees.
cos Z = ZY/XZ
cos Z = 5/ √34
Z = 30.96 degrees.
Thus, the value of the triangle are obtained.
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Calculate the area of the right triangle that has the following coordinates:
A: (-2,-1)
B: (1, 1)
C: (3,-2)
You must show all calculations to earn any credit. I suggest that you sketch this
triangle on graph paper so that the visual can help you.
The area of right triangle is [tex]\frac{1}{15}[/tex].
The given coordinates are [tex](-2,-1), (1, 1), (3,-2)[/tex].
We have to find the area of right triangle.
To find the area we first draw the graph using that coordinate.
The graph of the coordinate is
To find the area we use the formula
[tex]\angle ABC=\frac{1}{2}(|AB|)(|AC|)[/tex]
We first find the value of [tex](|AB|)[/tex] and [tex](|AC|)[/tex].
e coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]B[/tex] is [tex](1,1)[/tex].
The slope of [tex](|AB|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AB|)=\frac{1-(-1)}{1-(-2)}[/tex]
The slope of [tex](|AB|)=\frac{1+1}{1+2}[/tex]
The slope of [tex](|AB|)=\frac{2}{3}[/tex]
The coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]C[/tex] is [tex](3,-2)[/tex].
The slope of [tex](|AC|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AC|)=\frac{(-2)-(-1)}{3-(-2)}[/tex]
The slope of [tex](|AC|)=\frac{-2+1}{3+2}[/tex]
The slope of [tex](|AC|)=-\frac{1}{5}[/tex]
Now finding the area of right triangle by putting the values.
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times(-\frac{1}{5})[/tex]
Area can't be negative so
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times\frac{1}{5}\\\angle ABC=\frac{2}{30}\\\angle ABC=\frac{1}{15}[/tex]
Hence, the area of right triangle is [tex]\frac{1}{15}[/tex].
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Tell whether the triangle with the given side lengths is a right triangle. 18, 80, 82 Write the pythagorean theorem Substitute the values from the triangle in the equation then solve If both side of the equation is the same then yes the triangle is right triangle. Il both sides are different then no the triangle is not a right triangle
Pythagorean theorem :
c^2 = a^2 + b^2
Where:
c = hypotenuse (the longest side ) = 82
A & b = the other 2 sides (18 and 80)
Replacing:
82^2 = 80^2 + 18^2
Solve:
6,724 = 6,400+ 324
6,724 = 6,724
Both sides of the equations are equal. IT is a right triangle
57-92=17 -2c-ust +1 8x1322-1) = 677343 (x + 55-22-20 K 54+32--1 5x+363) = -1 5x+aen -6 8+2=6 2:6-8 -44)-5)-(2) 16-3942=12 18-y-18 -x-57-3222 - (-1)-sy-5633=2 2-35-17 = 2 2.3.3 -Byzo yo TARE 3) -x - 5y + z = 17 -5x - 5y +56=5 2x + 5y - 3z=-10 4) 4x + 4y + 2x - 4y+ 5x - 4y
ANSWER:
[tex]\begin{gathered} x=4 \\ y=2 \\ z=0 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 4x+4y+z=24\text{ (1)} \\ 2x-4y+z=0\text{ (2)} \\ 5x-4y-5z=12\text{ (3)} \end{gathered}[/tex]We solve by elimination:
[tex]\begin{gathered} \text{ We add (1) and (2)} \\ 4x+4y+z+2x-4y+z=24+0 \\ 6x+2z=24\text{ }\rightarrow x=\frac{24-2z}{6}\text{ (4)} \\ \text{ We add (1) and (3)} \\ 4x+4y+z+5x-4y-5z=24+12 \\ 9x-4z=36\text{ (5)} \\ \text{ replacing (4) in (5)} \\ 9\cdot(\frac{24-2z}{6})-4z=36 \\ 36-3z-4z=36 \\ -7z=36-36 \\ z=\frac{0}{-7} \\ z=0 \end{gathered}[/tex]Now, replacing z in (4):
[tex]\begin{gathered} x=\frac{24-2\cdot0}{6} \\ x=\frac{24}{6} \\ x=4 \end{gathered}[/tex]Then, replacing z and x in (1):
[tex]\begin{gathered} 4\cdot4+4y+0=24 \\ 16+4y=24 \\ 4y=24-16 \\ y=\frac{8}{4} \\ y=2 \end{gathered}[/tex]for the polyhedron, find the missing numberneed a whole number of faces
The Euler's polyhedron formula states that, for a polyhedron with F faces, E edges and V vertices, we have:
F + V - E = 2
For E = 12 and V = 6, then we have:
F + 6 - 12 = 2
F = 2 + 12 - 6
F = 8
Write the Distance Formula
Replace c with d to write the distance formula. Use the Distance Formula to Find the Distance Between Two Points
Find the distance, d, between G and H using the distance formula.
The distance between any two points (x1,y₁) and (x2,y2) on a
coordinate plane can be found by using the distance formula. Let (x,y)= (-2,1) and (x2,y2) =(4,-3). Substitute these values into the
distance formula and evaluate.
The distance between the two points is [tex]2\sqrt{13} units[/tex]
What is distance formula?
Distance formula is the measurement of distance between 2 points. It calculates the straight line distance between the given points. The formula can be given as [tex]distance=\sqrt{(c-a)^{2} +(d-b)^{2} }[/tex] Where A(a, b) B(c, d) Are the coordinates.
We are given the coordinates as (-2, 1) and (4, -3)
We substitute the values in the distance formula we get
[tex]distance=\sqrt{(c-a)^{2} +(d-b)^{2} } \\distance=\sqrt{(4+2)^{2} +(-3-1)^{2} }\\ distance=\sqrt{36+16 } \\distance=\sqrt{52 } \\distance =2\sqrt{13}[/tex]
Hence the distance between two points is [tex]2\sqrt{13} units[/tex]
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1. A table is 2 feet wide. It is 6 times as long as it is wide. Table= A-Label the diagram with the dimensions of the table.B-find the perimeter of the table
Width(w) = 2 feet
Length (L)= 6w = 6(2) = 12 feet
a. Table = 2 x 12
b: Perimeter of a rectangle:
P = 2w+ 2L = 2(2)+2(12) = 4+24 = 28 feet
Find the equation for the line that passes through the point (1,0), and that is perpendicular to the line with the
step 1
Find out the slope of the given line
we have
-(4/3)x+2y=4/3
isolate the variable y
2y=(4/3)x+(4/3)
Divide both sides by 2
y=(4/6)x+(4/6)
simplify
y=(2/3)x+(2/3)
the slope is m=2/3
Remember that
If two lines are perpendicular, then their slopes are negative reciprocal
that means
the slope of the perpendicular line to the given line is
m=-3/2
step 2
Find out the equation in slope-intercept form of the perpendicular line
y=mx+b
we have
m=-3/2
point ( 1,0)
substitute and solve for b
0=-(3/2)(1)+b
0=-(3/2)+b
b=3/2
therefore
the equation is
y=-(3/2)x+(3/2)ory=-1.5x+1.52x 5x+6 please simplify
Answer:
Step-by-step explanation:
Maybe
2x times 11x
Suppose you have 40 shirts and 15 pairs of pants to choose from in your wardrobe. Using the fundamental counting principle, how many outfit combinations are possible?
Type the correct answer in the box. Use numerals instead of words.
By taking the product between the number of shirts and pants, we coclude that there are 600 different outfit combinations.
How many outfit combinations are possible?
The total number of outfit combinations is given by the product between the numbers of each type of clothes that you have.
you have 40 shirts.
Yo have 15 pairs of pants.
Then the number of different combinations is 40*15 = 600
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