Answer: I am pretty sure you can only have one.
Step-by-step explanation:
The expression x^(3) gives the volume of a cube, where x is the length of one side of the cube. Find the volume of a cube with a side length of 2 meters.
Answer:
8 cubic meters
Explanation:
The length of one side of the cube = x
For any cube of side length, x:
[tex]\text{Volume}=x^3[/tex]Therefore, the volume of the cube with a side length of 2 meters is:
[tex]\begin{gathered} V=2^3 \\ =8\; m^3 \end{gathered}[/tex]In an electrical circuit, the voltage across a resistor is directly proportional to the current running through the resistor. If a current of 14 amps produces 280 volts across a resistor, how many volts would a current of 5.5 amps produce across an identical resistor?
A current of 5.5 amps produce across an identical resistor will produce 110Volts across an identical resistor
What is a current?From above,
Current 1 (I₁) = 14 amps
P.d (V₁) = 280 V
By Ohm's law which states that that for a linear circuit the current flowing through it is proportional to the potential difference across it so the greater the potential difference across any two points the bigger will be the current flowing through it.
V₁ = I₁R
= 280 = 14R
= 20Ω = R
Current 2 (I₂) = 3.5 A
Resistance (R) = 20 Ω
Assuming the resistance stays the same,
Using Ohm's law,
V₂ = I₂R
= 5.5*20
= 110 Volts
110Volts would be produced across an identical resistor
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IF G and R denote the grade and the radian measure of an angle, then prove that G/200 = R/pie
Solution:
Given;
IF G and R denote the grade and the radian measure of an angle, i.e.
Where
[tex][/tex]Look at the circle below. D = 6 3What is the area of the circle if the diameter is 6 centimeters? Use 3.14 for pi. A 18.84 square centimetersB 28.26 square centimeters C 37.68 square centimeters D 113.04 square centimeters
we are asked to determine the area of a circle with a diameter of 6 cm. To do that we will use the following formula for the area of a circle:
[tex]A=\frac{\pi D^2}{4}[/tex]Replacing the value of the radius:
[tex]A=\frac{\pi(6\operatorname{cm})^2}{4}[/tex]Replacing the value of pi:
[tex]A=\frac{3.14(6\operatorname{cm})^2}{4}[/tex]Solving the operations:
[tex]\begin{gathered} A=\frac{3.14(36cm^2)}{4} \\ \\ A=3.14(9cm^2)=28.26cm^2 \end{gathered}[/tex]How many modes does the following dataset have? 9,29,13,4,2,16,10,14,27
Given:
[tex]9,29,13,4,2,16,10,14,27[/tex]To find- the mode of the given dataset.
Explanation-
We know that the mode is the most occuring frequency of the dataset. Let us arrange the data in ascending order first, and we get
[tex]2,4,9,10,13,14,16,27,29[/tex]Since there is no repeated frequency, we can say that there is no mode for the given data set.
The answer is 0.
Solve the method.simultaneous equation by graphicaly + 3x = 6y - 2x = 1
The equations given are
[tex]\begin{gathered} y+3x=6............1 \\ y-2x=1............2 \end{gathered}[/tex]The graph of the equations will be shown below
Hence, the solution to the equations is the point where the two equations intersect.
Therefore, the solution is
[tex](1,3)[/tex]1. 3 In right AXYZ, the length of the hypotenuse YZ is 85 inches and tan Z= 3/4 What is the length, in inches, of the leg XY?
We have a right triangle XYZ.
The length of the hypotenuse is YZ=85.
We also know that the tangent of Z is 4.
We have to find the length of XY.
We can start by drawing the triangle and writing the data:
The tangent of an angle can be related with the sides by the following trigonometric ratio:
[tex]\tan (Z)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{XY}{XZ}=\frac{3}{4}[/tex]We can not find the value of the legs from the trigonometric ratio, but we have a proportion between them. We can write the previous result as:
[tex]\begin{gathered} \frac{XY}{XZ}=\frac{3}{4} \\ XZ=\frac{4}{3}\cdot XY \end{gathered}[/tex]Now we can relate XY with the hypotenuse YZ using the Pythagorean theorem:
[tex]\begin{gathered} XY^2+XZ^2=YZ^2 \\ XY^2+(\frac{4}{3}XY)^2=YZ^2 \\ XY^2+\frac{16}{9}XY^2=YZ^2 \\ (\frac{16}{9}+1)XY^2=YZ^2 \\ \frac{16+9}{9}XY^2=YZ^2 \\ \frac{25}{9}XY^2=YZ^2 \\ XY^2=\frac{9}{25}YZ^2 \\ XY=\sqrt[]{\frac{9}{25}YZ^2} \\ XY=\frac{3}{5}YZ \\ XY=\frac{3}{5}\cdot85 \\ XY=51 \end{gathered}[/tex]Answer: the length of the leg XY is 51 inches.
Someone please help me with this
Polynomial equations are those created using exponents, coefficients, and variables. It may have several exponents, with the higher one being referred to as the equation's degree.
How are polynomial equations solved?Polynomial equation illustration
Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.
6h²(5 + 9h)(5 - 9h)
6h²(9h + 5)(5 - 9h)
6h²(9h + 5)(-9h + 5)
Distribute6h²(9h + 5)(-9h + 5)
54(-9h +5)h³ + 30(-9h + 5)h²
(-486h)4 + 270h³+30(-9h+5)h²
(-486h)4 + 270h³-270h³+150h²
(-486h)4 + 150h²
Solution(-486h)4 + 150h²
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Reba is playing on the slide. Over and over, she climbs the 9-foot ladder, goes down the slide, and walks 3 feet to get back to the ladder. How far does Reba travel each time she repeats this process? If necessary, round to the nearest tenth.
we have
then find c
[tex]\begin{gathered} c^2=3^2+9^2 \\ c^2=9+81 \\ c^2=90 \\ c=\sqrt[]{90} \\ c=3\sqrt[]{10} \end{gathered}[/tex]therefore the distance is:
[tex]9+3\sqrt[]{10}+3=21.5[/tex]answer: 21.5 ft
The measures of the angles of a triangle are shown in the figure below. Solve for x. (2x+6)° 42°
A triangle is a shape that has a total angle of 180°.
How to solve the triangle?It's important to note that a triangle is a shape that has three sides and the total sum is equal to 180°.
In this case, we have 2x + 6 and 42°. The other angle isn't given and this can't be solved further
The sides will have been illustrated as:
= a + b + c = 180
The expression given will then be allocated for each side to solve it further.
Note that an overview was given as the information is incomplete.
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A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t) = (944)3 t/3, where t represents the number ofyears from the time of introduction.What is the tripling-time for this population of deer?
Ok, so
Here we have the function:
[tex]P(t)=944(3)^{\frac{t}{3}}[/tex]Now we want to find the tripling-time for this population of deer.
If we make t=0, we will find the initial population of deer. This is:
[tex]P(0)=944(3)^{\frac{0}{3}}=944[/tex]Now, we want to find the time "t" such that this population is the triple.
This is:
[tex]\begin{gathered} 944(3)=944(3)^{\frac{t}{3}} \\ 2832=944(3)^{\frac{t}{3}} \\ \frac{2832}{944}=3^{\frac{t}{3}} \\ 3=3^{\frac{t}{3}} \end{gathered}[/tex]We got this exponential equation:
[tex]3=3^{\frac{t}{3}}[/tex]As the base is the same, we could equal the exponents:
[tex]\begin{gathered} 1=\frac{t}{3} \\ t=3 \end{gathered}[/tex]Therefore, tripling-time for this population of deer are 3 years.
A computer part costs $7 to produce and distribute. Express the profit p made by selling 300 of these parts as a function of the price of c dollars. (Do not include $ symbol in your answer)
Given:
Each part costs $7 to produce and distribute.
The total number of parts on selling is 300 to make the profit P.
To write the function expression in terms of sale price C and profit P:
As we know,
[tex]\text{Profit}=\text{Selling price-cost price}[/tex]So, if we produce 1 part and sell that part, then the profit is
[tex]P=C-7[/tex]For 300 parts, the profit is
[tex]\begin{gathered} P=300(C-7) \\ P=300C-2100 \end{gathered}[/tex]Hence, the function is expressed in terms of P and C is,
[tex]P=300C-2100[/tex]Question 2 of 10The one-to-one functions g and h are defined as follows.g={(-8, 6), (-6, 7), (-1, 1), (0, -8)}h(x)=3x-8Find the following.g-¹(-8)=h-¹(x) =(hoh− ¹)(-5) =
Answer: We have to find three unknown asked quantities, before we could do that we must find the g(x) from the coordinate points:
[tex]\begin{gathered} g=\left\{\left(-8,6\right),(-6,7),(-1,1),(0,-8)\right\}\Rightarrow(x,y) \\ \\ \text{ Is a tabular function} \\ \end{gathered}[/tex]The answers are as follows:
[tex]\begin{gathered} g^{-1}(-8)=0\text{ }\Rightarrow\text{ Because: }(0,-8) \\ \\ \\ h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \\ \\ \\ \text{ Because:} \\ \\ h(x)=3x-8\Rightarrow\text{ switch }x\text{ and x} \\ \\ x=3h-8 \\ \\ \\ \\ \text{ Solve for }h \\ \\ \\ h=h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \end{gathered}[/tex]The last answer is:
[tex]\begin{gathered} (h\text{ }\circ\text{ }h^{-1})(-5) \\ \\ \text{ Can also be written as:} \\ \\ h[h^{-1}(x)]\text{ evaluated at -5} \\ \\ h(x)=3x-8 \\ \\ h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \\ \\ \\ \therefore\Rightarrow \\ \\ \\ h[h^{-1}(x)]=3[\frac{x}{3}+\frac{8}{3}]-8=x+8-8=x \\ \\ \\ \\ h[h^{-1}(x)]=x \\ \\ \\ \\ h[h^{-1}(-5)]=-5 \end{gathered}[/tex]f(x) = 3x² + 9x – 16
Find f(-8)
Answer: 104
Step-by-step explanation:
[tex]f(-8)[/tex] represents [tex]f(x)[/tex] evaluated at [tex]x=-8[/tex].
[tex]f(-8)=3(-8)^2 +9(-8)-16\\\\=192-72-16\\\\=120-16\\\\=104[/tex]
What value of Y makes this equation true?6y/-2 = 8 (-4/2)
Step 1
Given;
[tex]\frac{6y}{-2}=8(-\frac{4}{2})[/tex]Required; To find the value of y that makes the equation true
Step 2
Find the value of y
[tex]\begin{gathered} \text{Simplify} \\ -3y=4(-4) \end{gathered}[/tex][tex]\begin{gathered} \text{expand} \\ -3y=-16 \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by -3} \\ \frac{-3y}{-3}=\frac{-16}{-3} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplify} \\ y=\frac{16}{3} \end{gathered}[/tex]Hence, the value of y that makes the equation true is 16/3
Choose the left side that makes a True statement, and shows at the sum of the given complex numbers is 10Choose the left side that makes a true statement, and shows that the product of the given complex numbers is 40
For statement one:
We need to add up to complex numbers and their sum must give us equal to 10.
Also, we need to use the complex numbers:
5+i√15 and 5-i√15.
Then, we can use:
(5+i√15)+( 5-i√15) =
5+i√15+5-i√15 =
5+5+ i√15-i√15 =
= 10 + 0
= 10
For the second statement:
We need to show the product of complex numbers:
Then, we use:
(5+i√15)(5-i√15))=
5*5 - 5*i√15) +5*i√15) +√15*√15=
25 + 0 + 15=
40
The average number of moves a person makes in his or her lifetime is 12 and the standard deviation is 3.1. Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answers to four decimal places and intermediate z value calculations to two decimal places.Find the probability that the mean of a sample of 25 people is less than 10.Find the probability that the mean of a sample of 25 people is greater than 10.Find the probability that the mean of a sample of 25 people is between 11 and 12.
The z-score is given by the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where x is the data point, μ is the mean, and σ is the standard deviation.
First
on a cold January day , Mavis noticed that the temperature dropped 21 degrees over the course of the day to -9C. Write and solve an equation to determine what the temperature was at the beginning of the day
Answer:
Step-by-step explanation:
At the beginning of the day, the temperature was of x.
It dropped 21 degrees to -9C. So
x - 21 = -9
x =
a regular octagon has an area of 49 m 2 . find the scale factor of this octagon to a similar octagon with an area of 100 m 2
Given,
The area of the regular octagon is 49 square metre.
The area of the another regular octagon is 100 square metre.
[tex]\begin{gathered} \text{Scaling factor=}\frac{\sqrt{\text{area of regular polygon}}}{\sqrt[]{\text{area of another regular plogon}}\text{ }} \\ \text{Scaling factor=}\frac{\sqrt[]{\text{4}9}}{\sqrt[]{\text{1}00}\text{ }} \\ \text{Scaling factor=}\frac{7}{10\text{ }} \end{gathered}[/tex]Here, the scaling factor of the regualar octagon is 7:10
Hence, the scaling factor is 7:10.
Find the value of m and n that prove the two triangles are congruent by the HL theorem.
If both triangles are congruent by the HL theorem, then their hypotenuses are equal and at least one of the corresponding legs is equal too.
Hypothenuses:
[tex]13=4m+1[/tex]From this expression, you can calculate the value of m
[tex]\begin{gathered} 13=4m+1 \\ 13-1=4m \\ 12=4m \\ \frac{12}{4}=\frac{4m}{4} \\ 3=m \end{gathered}[/tex]Legs:
[tex]2m+n=8m-2n[/tex]Replace the expression with the calculated value of m
[tex]\begin{gathered} 2\cdot3+n=8\cdot3-2n \\ 6+n=24-2n \end{gathered}[/tex]Now pass the n-related term to the left side of the equation and the numbers to the right side:
[tex]\begin{gathered} 6-6+n=24-6-2n \\ n=18-2n \\ n+2n=18-2n+2n \\ 3n=18 \end{gathered}[/tex]And divide both sides of the expression by 3
[tex]\begin{gathered} \frac{3n}{3}=\frac{18}{3} \\ n=6 \end{gathered}[/tex]So, for m=3 and n=6 the triangles are congruent by HL
In a competition of 837 people, Jenny scored at the 77th percentile.
In what place did she finish?
Answer:
Jenny scored 644th place.
Step-by-step explanation:
To find out what place she finished, you need to write it out first like this:
77% of 837.
Now, to make the equation possible to solve, we can take the 77 and make it a decimal: 0.77.
The term "of" means multiplication.
So, in turn, we have the equation:
0.77 x 837 = 644.49
And, if you round it, your answer would be:
Jenny scored 644th place.
Answer:
See below
Step-by-step explanation:
77th percentile means she scored better than 77 per cent of the test takers...
So Jenny's place was .23 * 837 = ~ 193 rd Out of 837 people
The absolute value of 1/4
Answer: 1/4 is the absolute
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
Absolute value just means the distance from zero.
work out sues total pay
Sue's total pay for the year given the salary, bonus and share of profit is £38,110.
What is the total pay?Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.
Salary for the year = monthly salary x number of months in a year
£1410 x 12 = £16,920
The next step is to determine the profit last year
Profit = total revenue - total cost
£549,000 - £473,500 = £75,500
Now determine the share of profit that Sue would earn.
Share of profit = 26% x £75,500
0.26 x £75,500 = £19,630
Now determine the total bonus she would earn : 4 x £390 = £1560
Total salary = £1560 + £19,630 + £16,920 = £38,110
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Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
Answer:
There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.
Step-by-step explanation:
the water pressure on Mustafa as he dives is increasing at a rate of 0.992 atmospheres (atm) per meter
What is the rate of increase in water pressure in atm/km
The rate of increase in water pressure in atm/km = 992 atm/km
what is pressure?Pressure can be defined as the external or internal force that acts on an area of an object which can be measured in atmosphere per meter.
The rate at which Mustafa dives = 0.992atm/meter.
That is,
0.992 atm = 1 meter
X atm = 1 km
But 1000m = 1 km
make X atm the subject of formula;
x atm = 0.992 × 1000
X atm = 992 atm/km
Therefore, the rate in atm/ km would be = 992 atm/km
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The length of the longest slide is what inches the other two sides will each be what inches in length?
We know that the rod from which we made the triangle is 13 in long, this means that the perimeter of the triangle. from the diagram given we notice that the perimeter is:
[tex]x+(x-1)+(x-1)[/tex]equating this to 13 and solving for x we have:
[tex]\begin{gathered} x+(x-1)+(x-1)=13 \\ 3x-2=13 \\ 3x=13+2 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5 \end{gathered}[/tex]Hence, the value of x=5 which means that the longest side measure 5 inches. To determine the length of the other sides we notice that they are given by x-1, which means that their length is 5-1=4 inches,
Therefore, the length of the longest side is 5 inches. The other two sides will each be 4 inches in length.
Labron James made 255/310 baskets. What percent of the baskets did he make?
82.26%
Explanations:The ratio of baskets made by Lebron James = 255/310
To find the percentage equivalent of the ratio, multiply it by 100%
Percentage of the baskets made by Lebron James = 255/310 x 100%
Percentage of the baskets made by Lebron James = 82.26%
&A(n)is formed when two rays have a common endpoint.Oline segmentangle
When two rays are with a common endpoint, an angle is formed and the common endpoint is called the vertex of the angle
NO LINKS!! Please help me with this probability question 3a
Answer:
b) 26%
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
[tex]\textsf{Mean}\;\mu=3550[/tex]
[tex]\textsf{Standard deviation}\:\sigma=870[/tex]
Therefore, if the weights of the cars passing over the bridge are normally distributed:
[tex]\boxed{X \sim\text{N}(3550,870^2)}[/tex]
where X is the weight of the car.
To find the approximate probability that the weight of a randomly-selected car passing over the bridge is less than 3000 pounds, find[tex]\text{P}(X < 3000)[/tex].
Calculator input for "normal cumulative distribution function (cdf)":
Upper bound: x = 3000Lower bound: x = –9999...μ = 3550σ = 870[tex]\implies \text{P}=0.2636333503[/tex]
[tex]\implies \text{P}=26\%[/tex]
Therefore, the approximate probability that the weight of a randomly-selected car passing over the bridge is less than 3000 pounds is 26%.
If AACB = ADCE, ZCAB = 63°,ZECD = 52°, and ZDEC = 5xDE(c сx = [?]
Since angles ACB and ECD are vertical angles, they are congruent, so we have
Calculating the sum of internal angles in triangle ABC, we have:
[tex]\begin{gathered} ABC+ACB+CAB=180 \\ ABC+52+63=180 \\ ABC=180-52-63 \\ ABC=65 \end{gathered}[/tex]Since triangles ACB and DCE are congruent, we have [tex]\begin{gathered} DEC=ABC \\ 5x=65 \\ x=13 \end{gathered}[/tex]
