Answer: [tex]\frac{3}{10}[/tex] or 30%
Step-by-step explanation:
We will divide the wanted outcomes by the possible outcomes.
[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{number of prime number}}{\text{number of numbers 1 through 50}} =\frac{15}{50}=\frac{3}{10}\;\; \text{or 30\%}[/tex]
The prime numbers from one through fifty are; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
-> This is 15 numbers
The width of a straight racetrack is one tenth of the measurement of its length, the perimeter of the track is 132 meters, what are the dimensions of the length and width of the track?
Step-by-step explanation:
L = 10W
L + W = 132/2 = 66
---
10W + W = 66
W = 6
L = 60
[tex] \sf{\red{Answer}} [/tex]
L = 60 mW = 6 m[tex] \sf{\purple{Step \: \: By \: \: Step \: \: Explanation}} [/tex]
Perimeter = 2(L + W)
132 = 2(L + L/10)
132 = 2(10L/10 + L/10)
132 = 2(11L/10)
132 : 2 = 11L : 10
66 = 11L : 10
66 : 11 = L : 10
6 = L : 10
L = 6 × 10 = 60 mW = L/10 = 60/10 = 6 m GEOMETRY)
In the figure, chords AB and CD intersect at E. If the measure of arc AC is 30 degrees and the m angle DEB=80^o , then find the degree measure of arc DB
Enter just a number for your answer
(Picture is below) thank you!
Answer: 130
Step-by-step explanation:
Let the measure of arc DB be x.
Then,
[tex]80=\frac{x+30}{2}\\\\160=x+30\\\\x=130[/tex]
3 multiply by what is equal to 30 plus what
Call the hidden variable here "x"
3x = 30 + x
3x - (30 + x) = 0
3x - 30 - x = 0
2x - 30 = 0
x = 30 : 2 = 15
Recheck : 3 x 15 = 30 + 15 -> 45 = 45 (true)
You are going to paint a six-sector spinner. There are 4 colors to choose from. How many different ways can you paint the spinner if each color can be used more than once and no two adjacent sectors can be the same color?
Using the Fundamental Counting Theorem, it is found that there are 648 ways to paint the spinner.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem, we have that the first sector can be painted in any of the 4 colors, the others until the 5th can be painted in 3 colors(not the adjacent), and the sixth in only 2, as it is adjacent to both the 5th and the 1st sectors, hence:
[tex]n_1 = 4, n_2 = n_3 = n_4 = n_5 = 3, n_6 = 2[/tex]
Hence the number of ways is given by:
N = 4 x 3 x 3 x 3 x 3 x 2 = 648.
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How do I decide if it’s a real solutions or extraneous solutions?
Step-by-step explanation:
So you can check for extraneous solutions by plugging in the 5 and -2 as x.
Plug 5 in as x
[tex]5=\sqrt{3(5)+10}\\5=\sqrt{15+10}\\5=\sqrt{25}\\5=5[/tex]
I'm not sure if this is exactly considered an extraneous solution, but I'm assuming it is, since technically the radical doesn't have a plus/minus in front of it, so it's the principle square root which means it only outputs the positive values. This would mean that the -2 wouldn't be a solution, since the principle square root doesn't output negative values, so it's a function, since if it outputted 2 values, then it wouldn't be a function by definition.
Triangle A B C is shifted to the left to form triangle A prime B prime C prime. Triangle A prime B prime C prime is then dilated to form larger triangle A double-prime B double-prime C prime.
Determine the similarity transformations that verify △ABC ~ △A''B''C'.
The first transformation mapping △ABC to △A'B'C' is a
.
The second transformation mapping △A'B'C' to △A''B''C' is a
.
Similarity transformations involve two types of transformations required to map a given object onto a similar object without a change in its dimensions. Thus the answers required are:
a. Similarity transformations - translation and dilation.
b. The first transformation is translation.
c. The second transformation is dilation.
Transformation is a process required to change the size or orientation of a given shape to form an image. The types are reflection, translation, rotation, and dilation.
i. Reflection is a type of rigid transformation in which a given shape is flipped about a given point or line.
ii. Translation involves moving a given shape in a certain direction without a change in its initial orientation.
iii. Rotation is a type of rigid transformation where a shape is turned about a given point or line at a required angle.
iv. Dilation is a process that requires either increasing or decreasing the dimension of a given shape.
Also, similarity transformations involve two types of transformations required to map a given object onto a similar object without a change in its dimensions.
The appropriate answers to the given question are:
a. similarity transformations - translation and dilation
b. The first transformation is translation.
c. The second transformation is dilation.
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In the following exercises, solve
636. The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of 29.5 liters with 2000 psi, what is the volume if the tank has a 14.7 psi rating? Round to the nearest whole number
Answer:
When the volume of a gas in a container varies inversely with the pressure on the gas and a container of nitrogen has a volume of 29.5 litres with 2000 psi. So, if the tank has a 14.7 psi pressure, then the volume of the tank would be 4013.6 litres.
Step-by-step explanation:
The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of litres with psi, what is the volume if the tank has a psi pressure.Calculate the volume to the nearest whole number.Use the given values and calculate the proportionality constant as well as required solution.Step 1 of 2
Write the inversely proportionality relation between the volume and pressure of a gas in container.
[tex]$v \propto \frac{1}{p}$[/tex]
Where volume is represented by v and pressure is represented by p.
Remove the proportionality and place a constant say k.
[tex]$v=\frac{k}{p}$[/tex]
Substitute the given values of nitrogen that v=29.5 and
p=2000 and calculate the value of k from above equation.
[tex]$$\begin{aligned}&29.5=\frac{k}{2000} \\&\Rightarrow k=29.5 \times 2000 \\&\Rightarrow k=59000\end{aligned}$$[/tex]
Step 2 of 2
Substitute the value p=14.7 and above calculated k value in the equation
[tex]$$\begin{aligned}&v=\frac{k}{p} . \\&v=\frac{59000}{14.7} \\&\Rightarrow v=4013.6\end{aligned}$$[/tex]
A diagonal matrix has the elements shown below.
211 = 16
a22-8.7
233= 5.4
a44 1.3
255=-6.9
Which is the diagonal matrix containing these elements?
16 -3.7 6 1.7 -8.8
0
-8.7 -4.14 1 7
0
0
5.4 -9 -3
0
0
0
1.3 5
0
0
0
0 -6.9
The diagonal matrix that has these values would be:
16 0 0 0 0
0 -8.7 0 0 0
0 0 5.4 0 0
0 0 0 1.3 0
0 0 0 0 -6.9
What is a diagonal matrix?This is the type of matrix that is written in the form where all of the entries that are outside the diagonal are zeros.
The diagonal is a line that divides a triangle into two halves. The diagonal here has all of the digits. Outside it are all zero elements.
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Answer:
C is the correct answer
Explanation:
Hope you have a great day!
HELP PLEASE!! x3-3x2-10x+24 by x-2. fill into other equation
The solution to the division of the given polynomial expression is:
k = (x+3)(x-4)
Division of polynomialsThe division of the given polynomial can be determined by using the rational root theorem which is a method that is popularly used in determining the solutions to a polynomial equation.
From the information given:
[tex]\mathbf{\dfrac{x^3 -3x^2 - 10x +24}{x-2}}[/tex]
Using the rational root theorem;
[tex]\mathbf{\dfrac{(x-2) \dfrac{x^3 -3x^2 - 10x +24}{x-2} }{x-2}}[/tex]
[tex]\mathbf{\dfrac{(x-2)(x^2 -x-12)}{x-2} }}[/tex]
Factor: x² - x - 12
[tex]\mathbf{\dfrac{(x-2)(x+3)(x-4)}{x-2} }}[/tex]
Cancel out the common factor (x-2)
[tex]\mathbf{=(x+3)(x-4) }}[/tex]
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Find the measure of the reference angle for an 11 radian
radian angle.
Answer:
about 1.56637 radians ≈ 89.746°
Step-by-step explanation:
The reference angle in radians can be found by the formula ...
ref angle = min(mod(θ, π), π -mod(θ, π))
Equivalently, it is ...
ref angle = min(ceiling(θ/π) -θ/π, θ/π -floor(θ/π))×π
ApplicationWhen we divide 11 radians by π, the result is about 3.501409. The fractional part of this quotient is more than 1/2, so the reference angle will be ...
ref angle = (1 -0.501409)π radians ≈ 1.56637 radians ≈ 89.746°
__
Additional comment
For calculations such as this, you need to use the most accurate value of pi available. The approximations 22/7 or 3.14 are not sufficiently accurate to give good results.
17. Two tanks are similar in shape. The capacity of the tanks are 1,000,000 litres and 512, 000 liters respectively
. a) Find the height of the smallest tank if the larger is 300cm tall .(4 marks)
The height of the smallest tank if the larger is 300cm tall will be 240cm.
What is the similarity?Similar figures are those figures which are identical in shape, but not necessarily in size.
Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.
We can utilize scale factors because the tanks have comparable shapes.
The scale factor for volume will be given as,
The volume of small tank/volume of big tank = 512000/1000000 = 0.512
Since volume, if the cube so,
Scale factor = [tex](0.512)^{1/3}[/tex] = 0.8
With this scale factor the height of the smaller tank = 300 x 0.8 = 240cm
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Does anyone know the answer? Please help.
Answer:
(0,-2)
Step-by-step explanation:
the answer is (0,-2) because -2 is where the line crosses over the y-axis. If we looked at a graph you would see that the line goes over 0 on the X-axis, which causes the line to touch the y-axis and intercept it at the -2 mark.
An easy way to find the answer for these sorts of questions is to draw out a graph and mark the coordinates on it and draw the line conecting them. Once you've done that you can easily see where the line intercepts on both the y and x axis.
Answer:
(0,-2)
please put brainliest
Plss help which is the same value as 20% of 45??
Answer:
A, B and D
Step-by-step explanation:
Answer:
Answer B , D , E
Step-by-step explanation:
Label the vertices and all the elements needed. find x. give reasons!
The value of x which is the missing angle of the triangles is; x = 30°
How to find the missing angles of a triangle?We know that Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
Thus, if we label the vertex with the unknown angle in the smaller triangle as A, then by the alternate angle theorem, we can say that;
∠A = 2x
Thus, from sum of angles in a triangle equals to 180°, we can say that;
x + 2x + 90 = 180
3x + 90 = 180
3x = 180 - 90
3x = 90
x = 90/3
x = 30°
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What are the solutions of the equation x4 3x2 2 = 0? use u substitution to solve.
The solution of the equation is x=±i or x=±i√2.
Given that the equation is x⁴+3x²+2=0 and use u substitution method to solve.
We can rewrite our given equation as:
(x²)²+3x²+2=0
Let's assume that the (x²)=u.
The given equation is rewritten as u²+3u+2=0.
Factorize the quadratic equation by adding or subtracting two number that gives the sum of 3u and product 2u² as
u²+2u+u+2=0
u(u+2)+1(u+2)=0
Taking out (u+2) as common and get
(u+2)(u+1)=0
Compare each equation with 0 and get
u+2=0 or u+1=0
u=-2 or u=-1
Performing back substitution by substituting the values of u in x²
when u=-1 then x is
x²=-1
x=±√(-1)
As we know that √(-1)=i.
So, we get
x=±i
And when u=-2 then x is
x²=-2
x=±√(-2)
As we know that √(-1)=i.
So, substituting this, we get
x=±i√2
Hence, the solutions of the x⁴+3x²+2=0 is x=±i and x=±i√2.
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Please help!! I have been stuck on this question for a while
Answer:
[tex]180\ in.^2[/tex]
Step-by-step explanation:
The area of a rectangle can is defined as [tex]A = wl[/tex] where w is the width and l is the length. The width in this case is 12 and the length is 15. Also it doesn't really matter what order you put it in. This gives you an area of [tex](15\ in.) (12\ in.) = 180\ in.^2[/tex]
An independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. They collected information on the percentage of the bill left as a tip for 35 randomly selected bills. The average tip was 14.2% of the bill with a standard deviation of 2.5%. Assume that the tips are approximately normally distributed. Construct an interval to estimate the true average tip (as a percent of the bill) with 99% confidence. Round the endpoints to two decimal places, if necessary.
An interval to estimate the true average tip is (14.62,13.78).
According to statement is
we know that the
confidence interval = sample mean ± standard deviation /(n)^1/2
substitute the values in it then
confidence interval = 14.2 ± 2.5/(35)^1/2
confidence interval = 14.2 ± 2.5/5.91
confidence interval = 14.2 ± 0.42
confidence interval = 14.2 + 0.42 , confidence interval = 14.2 - 0.42
confidence interval = (14.62,13.78)
So, an interval to estimate the true average tip is (14.62,13.78).
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please help
I don't know what im supposed to do.
Answer:
Step-by-step explanation:
You did not post any question and I just retrieved all possible information from whatever is given.
SOMEONE, PLEASE ANSWER THIS!
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
6 is added to the product of 7 and a number.
Answer:
Step-by-step explanation:
Solution
Start with the product
The product is 7*x where x is a number but not specified.
Now add 6
Answer: 7x + 6
This cannot be simplified any more than what it is now.
Represent the following sentences as an algebraic expression:
6 is added to the product of 7 and a number.Explanation -:Assuming:
Let us assume the number as x.6 is added to the product of 7 and a number.
Product : 7 × x = 7x
Now we will add 6.
Add : 7x + 6.
Final Answer:
7x + 6.
[tex] \star\tiny\pmb{spbankingandsscseries} \small\star [/tex]
A right triangle is shown. The other 2 angles are 45 degrees. The length of the hypotenuse is 24 inches.
The hypotenuse of a 45°-45°-90° triangle measures 24 inches. What is the length of the one leg of the triangle?
12 in.
12 StartRoot 2 EndRoot in.
24 in.
24 StartRoot 2 EndRoot in.
The length of one leg of the right triangle is h = 12√2 inches
How to find the length of the leg of a right triangle?The length of a right triangle can be found as follows;
sin 45 = opposite / hypotenuse
Therefore,
hypotenuse = 24 inches
Hence,
sin 45 = h / 24
h = 24 sin 45
h = 24 × 1 / √2
Therefore,
h = 24 / √2 × √2 / √2
h = 24√2 / 2
h = 12√2 inches
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Answer: B. 12√2 inches
Step-by-step explanation: TRUST ME!!! Answer correct on Edge!!! :)
Solve 2x²+x-4 = 0.
²+1/2
1
2
x² +
23
x + -2
x + 2
Answer:
[tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex]
Step-by-step explanation:
Hello!
We can solve the quadratic by using the Quadratic Formula.
Standard form of a Quadratic: [tex]ax^2 + bx +c = 0[/tex]
Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Given our equation: [tex]2x^2 + x - 4 = 0[/tex]
a = 2b = 1c = -4Plug in the values into the quadratic formula to solve.
Solve the quadratic[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-1 \pm \sqrt{1^2 - 4(2)(-4)}}{2(2)}[/tex][tex]x = \frac{-1 \pm \sqrt{1 + 32}}{4}[/tex][tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex]The solution to the quadratic is [tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex].
Which of the following lists of ordered pairs is a function?
OA. (0, 2), (4, 2), (0, -4), (4, -2)
OB. (2, 4), (3, 9), (4, 16), (5, 25)
O C. (1, 1), (2, 3), (1, 5), (4,7)
OD. (2, 4), (-2, 4), (3, 9), (-2,-4)
Answer:
OB. (2, 4), (3, 9), (4, 16), (5, 25)
Step-by-step explanation:
none of the points in this ordered pair have the same x-pos. In all the other options, at least 2 of the points have the same x-pos, preventing them from being functions. Therefore, OB is the only right answer.
Please mark brainliest!!!!!!!!Each container will be made of a material that costs $0.0015 per square inch. Explain how to determine the coat of each container. Then find the cost of Container b. Round to the nearest cent.
Answer:
Find total surface area. Multiply material unit cost by the total surface area.
Step-by-step explanation:
To find the cost of a container, you must first find the total surface area of the container. Then since you are given the unit cost for the material, you multiply the total surface are by the unit cost ($0.0015/in.²).
URGENT:Two publishers have offered Dr. Spencer Lewis, a noted dietician, a deal on his new book Don't Dig Your Grave with Your Knife and Fork. The first has offered to pay him $50,000 up front and a $3 royalty for every book it sells. The second has offered to pay $20,000 up front and a $5 royalty for every book it sells. Over what range of sales will Dr. Lewis make more from the deal with the second company than he will from the deal with the first?
The range of sales Dr. Spencer Lewis must exceed to profit the most from the second deal is 15,000 sales.
How to find the range of sales that favors Dr. more with the second deal?To find the range that will benefit Dr. Spencer Lewis the most with the second deal, we must perform the following operation:
A. X × 5 + 20,000B. X × 3 + 50,000We must replace the X with several numbers and buy the result, when the result of operation B exceeds the result of operation A, it means that it will be more profitable.
According to the above, if we replace the X with 15,000, the values will be the same, however, each number that we increase will mean a greater profit in agreement B.
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log 2x + log x = 2
What is the answer
Answer:
x=5[tex]\sqrt{2\\[/tex]
Step-by-step explanation:
Answer:
5 sqrt 2
Step-by-step explanation:
Log 2x + log x = 2
log ( 2x * x ) = 2
log (2x^2) = 2
2x^2 = 100
x^2 = 50
x = sqrt (50) = 5 sqrt 2
Simplify the following expressions.
The simplified expression for the following expression are:
7a + 3a - 2a + 5a = 13a0.7 - 0.3g - 0.02g + 5 = 5.7 - 0.32g5g² + 3g - 4g + 5g² = 10g² - gSimplification7a + 3a - 2a + 5a
= 15a - 2a
= 13a
0.7 - 0.3g - 0.02g + 5
= 5.7 - 0.32g
5g² + 3g - 4g + 5g²
= 10g² - g
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Please Help me, Asap, want to get as ahead as possible in math before school starts.
The measure of angle ABD (m∠ABD) is 104°
Calculating the measure of anglesFrom the question, we are to determine the measure of angle ABD
In the diagram,
∠ABC = ∠ABD + ∠DBC
Thus,
m∠ABC = m∠ABD + m∠DBC
From the given information,
m∠ABC = 140°
m∠DBC = 36°
∴ 140° = m∠ABD + 36°
m∠ABD = 140° - 36°
m∠ABD = 104°
Hence, the measure of angle ABD (m∠ABD) is 104°
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Select the correct answer.
Which equation represents a line that is perpendicular to line PQ?
A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line falls through two closed points P (negative 8, 7), and Q (negative 4, negative 5).
A. y=3x-2
B. y=1/3x+4
C. y=1/3x-5
D. y=-3x+6
A perpendicular line to PQ must have a slope equal to 1/3, then the correct options are B and C.
Which equation represents a line that is perpendicular to line PQ?Two lines are perpendicular if the slope of one is equal to the opposite of the inverse of the other line's slope.
We know that PQ passes through (-8, 7) and (-4, 5), then the slope of PQ is:
[tex]s = \frac{-5 - 7}{-4 - (-8)} = -3[/tex]
A perpendicular line to PQ must have a slope equal to:
[tex]s' = -(\frac{1}{-3} ) = (\frac{1}{3})[/tex]
So we have two correct options (two lines with that slope) which are options B and C.
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If Elon and Jeff work together, they can finish the work in 3 hours. If Jeff works together with Bruce, they can make this work done in 6 hours. Elon and Bruce can finish this work in 4 hours. How much time would it take to finish the work if all three worked together?
Answer:
It would take 1.5 hours for all three to finish the work if they worked together.
Step-by-step explanation:
Elon and Jeff can complete the work in 3 hours.
Jeff and Bruce can complete the work in 6 hours.
Elon and Bruce can complete the work in 4 hours.
3 + 6 + 4 = 13
13 / 3 = 4.33
4.33 / 3 = 1.44
Consider the function.
Match each transformation of f(x) with its description.
stretches f(x) by a factor
of 4 away from the x-axis
shifts f(x) 4 units down
shifts f(x) 4 units right
compresses f(x) by a factor
of toward the y-axis
The correct options are:
a) g(x) = 8*x - 6
b) g(x) = 2x - 10
c) g(x) = 2x - 14
d) g(x) = 8x - 24
How to identify each transformation?Here we have the function:
f(x) = 2x - 6
The proposed transformations are:
a) Stretch by a factor of 4 along the x-axis.
A horizontal stretch of scale factor k is written as:
g(x) = f(x*k).
Then, in this case, we have:
g(x) = 2(x*4) - 6 = 8*x - 6
b) Shift f(x) 4 units down.
A vertical shift of N units is written as:
g(x) = f(x) + N
A shift of 4 units down is written as:
g(x) = f(x) - 4 = 2x - 6 - 4 = 2x - 10
c) Shift f(x) 4 units right.
An horizontal shift of N units is written as:
g(x) = f(x + N).
For a shift of 4 units to the right, we write:
g(x) = f(x - 4) = 2(x - 4) - 6 = 2x - 8 - 6 = 2x - 14
d) A vertical compression of scale factor 1/4.
A vertical compression of scale factor K is written as:
g(x) = f(x)/K
In this case, we will have:
g(x) = f(x)/(1/4) = 4*f(x) = 4*(2x - 6) = 8x - 24
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