SOLUTION
We have been given the circumfeence of the circle as 56.52 and we are told to find the diameter
Circumference of a circle C is found as
[tex]\begin{gathered} C\text{ }=\pi d \\ \text{Where }\pi\text{ = 3.14 and d is the diameter. So from } \\ C\text{ }=\pi d \\ 56.52\text{ }=3.14d \\ d\text{ = }\frac{56.52}{3.14} \\ \\ d\text{ = 18} \end{gathered}[/tex]Therefore, the diameter is 18
23 pointsThe length of a rectangular box is 1 inch longer than twice the width (x).The height is 5 inches.which is the volume (y) function
y = 5x ( 2x + 1)
Explanations:Let the width of the rectangular box be x
Let the length be L
Let the height be H
Let the volume be y
The length of the rectangular box is 1 inch longer than twice the width (x)
L = 2x + 1
The Height is 5 inch
H = 5
The volume of a rectangular box is:
Volume = Length x Width x Height
y = LHx
y = (2x + 1) (5) (x)
y = 5x (2x + 1)
This pentagonal prism is cut by the plane shown. The plane is parallel to the base of the pentagonal prism. What is the shape of the cross-section?
If the plane is parallel to the base, then the cross section has the same shape of the base: a penthagon.
a farmer wants to build a fence in the shape of a parallelogram for his animals. The perimeter of the fence will be 600 feet, and the North/South fences are half of the length of the West/East fences. If fences are sold in 5 foot segments, how many fence segments does the farmer need to buy ?
Let's use the variable L to represent the length and W to represent the width.
If the perimeter is 600 ft, we have:
[tex]\begin{gathered} P=2L+2W\\ \\ 2L+2W=600\\ \\ L+W=300 \end{gathered}[/tex]The width is half the length, so we have:
[tex]\begin{gathered} W=\frac{L}{2}\rightarrow L=2W\\ \\ 2W+W=300\\ \\ 3W=300\\ \\ W=\frac{300}{3}\\ \\ W=100\text{ ft}\\ \\ L=200\text{ ft} \end{gathered}[/tex]Now, if each fence segment is 5 ft, we number of segments needed is:
[tex]\begin{gathered} \text{ fences for W1: }\frac{100}{5}=20\\ \\ \text{ fences for W2: }\frac{100}{5}=20\\ \\ \text{ fences for L1:}\frac{200}{5}=40\\ \\ \text{ fences for L2:}\frac{200}{5}=40\\ \\ \\ \\ \text{ total:}20+20+40+40=120\text{ fence segments} \end{gathered}[/tex]A = bh; solve for h
Given the equation:
[tex]A=b\cdot h[/tex]It's required to solve it for h, that is, isolate h as the only letter on the left side of the equation.
First, swap sides.
[tex]b\cdot h=A[/tex]Then, divide both sides of the equation by b:
[tex]\frac{b\cdot h}{b}=\frac{A}{b}[/tex]Simplify the left side:
[tex]h=\frac{A}{b}[/tex]picture with question
In order to determine if the given triangles are similar, it is necessary to find the values of the missing angles.
Take into account that the sum of the interior angles of a triangle is equal to 180°, the for the missing angles you have:
180° - 90° - 46° = 44°
180° - 38° - 46° = 96°
AS YOU CAN NOTICE THE THREE ANGLES ARE NOT EQUAL.
Then, the triangles are NOT similar because it is necessary that the three angles are equal.
The side lengths of a triangle are shownbelow. How many other triangles with thesemeasurements could be made?A. None just this unique triangleB. Two trianglesC. Many triangles84 mm96 mm60 mm
Given the side lengths of some triangle:
[tex]\begin{gathered} L_1=84 \\ L_2=96 \\ L_3=60 \end{gathered}[/tex]Let us suppose that there exists another triangle with these side lengths:
[tex]\begin{gathered} L_1^{\prime}=84 \\ L_2^{\prime}=96 \\ L_3^{\prime}=60 \end{gathered}[/tex]Based on these, we can say that:
[tex]\begin{gathered} L_1\cong L_1^{\prime} \\ L_2\cong L^{\prime}_2 \\ L_3\cong L^{\prime}_3 \end{gathered}[/tex]Then, using the Side-side-side theorem, we conclude that both triangles are congruent, so this triangle is unique
The braking distance of a car is proportional to the square of its speed.17. According to Graham's law, the rate of diffusion of two gases is inverselydproportional to density and is given bywhere ', and r2 are12rates of diffusion of two gases and d, and d2 are their respectivedensities. Which equation represents d, in terms of the other variables?
Ok in this problem you have to take Graham's law which is given to you and manage to write the density d1 as a function of the others. We have:
[tex]\frac{r_1}{r_2}=\sqrt[]{\frac{d_2}{d_1}}[/tex]Since we want to have d1 alone in one side of the equation the first thing we have to do is pass the square root to the other side. Square roots pass as square powers:
[tex](\frac{r_1}{r_2})^2=\frac{d_2}{d_1}[/tex]Then we have to pass d1 multiplying on the other side:
[tex]d_1\frac{r^2_1}{r^2_2}^{}=d_2[/tex]Now we only need to pass both r1 and r2:
[tex]d_1=d_2\frac{r^2_2}{r^2_1}[/tex]This is the same expresion that the one in item B so that is the correct answer
Which expression is a factor of 9r2 – 4r + 1? F3r-1 Gr 1 H 9741 3 There are no real factors.
There are no real factors
Here, we want to factorize the given expression
To check if there are real factors, we will need to get the determinant
mathematically, we have this as;
[tex]D=b^2-4ac[/tex]where a is 9, b is -4 and c is 1
Substituting these values;
[tex]D=(-4)^2-4(9)(1)\text{ = 16-36 = -20}[/tex]As we can see, the value of the determinant is negative
Whenever the determinant value is negative, there are no real roots
What is the solution to the equation 3^x = 10?
Start by applying the log on both sides wi
What is the value of x?x = ___ ydRound your answer to the nearest tenth
We need to use the cosine of the angle, in this case:
Cos(37°) = 30 yd / X
Thus, X = 30 / Cos(37) = 30 / 0.7986 = 37.56
Complete the function table.Input (n) Output (n + 5)-242
Answer
To complete the table, you need to substitute the values of the inputs (n) given into the output (n+5) given.
A pizza restaurant has found that the probability that a customer will order thin crust is 0.4. In a random sample of 5 customers who order a pizza, find the probability that at least three of them want thin crust.
In this type of exercises, the probability of x successes on n reapeted trials in an experiment is given by the next formula:
[tex]P=\text{nCx}\cdot p^x\cdot(1-p)^{n-x}[/tex]Here the nCx indicates the number of different combinations of x objects selected from a set of n objects. With the given data we can solve it easily:
p = 0.4
n = 5
x = 3
[tex]\begin{gathered} P=5\text{C3}\cdot0.4^3\cdot(1-0.4)^{5-3} \\ P=10\cdot0.064\cdot0.36 \\ P=0.2304 \end{gathered}[/tex]A 8 kg eagle is flying up in the sky. You pull out your GPE gun and are able to tell that the bird has a GPE of 2,352 J. How high must the birdbe? (remember the bird is on Earth)
Energy = work per unit time
Energy = workdone / time
energy = mgh
m = 8kg
E = 2352J
since the bird is on the earth, definitely the gravitational force will be acting on it
g = 10m/s^2
2352 = 8 x 10 x h
2352 = 80 x h
2352 = 80h
divide both sides by 80
2352/80 = 80h/80
29.4 metres = h
h = 29.4 metres
The answer is 29.4 metres
Find a linear equation satisfying the condition, if possible. Passes through (−1,5) and (0,10)
The linear equation has the coordinates (−1,5) and (0,10) ,
[tex]y-5=\frac{10-5}{0+1}(x+1)[/tex][tex]y-5=\frac{5}{1}(x+1)[/tex][tex]y-5=5x+5[/tex][tex]y=5x+10[/tex]Hence , the linear equation is y=5x+10.
Consider the line y=x+3.Find the equation of the line that is parallel to this line and passes through thepoint (-6, -3).Find the equation of the line that is perpendicular to this line and passes throughthe point (-6, -3).
Given:
Consider the line y=x+3.
Required:
We want to Find the equation of the line that is parallel to this line and passes through the point (-6, -3).
Find the equation of the line that is perpendicular to this line and passes through the point (-6, -3)
Explanation:
To find parallel to this line and passes through the point (-6, -3)
The slope is same for parallel line is 1
[tex]\begin{gathered} y-(-3)=1(x-(-6)) \\ y+3=x+6 \\ y=x+3 \end{gathered}[/tex]Which is same so there is no parallel line of given line which is passes through point (-6, -3)
Now to find the perpendicular to the given line
for this the slope of this line is -1
[tex]\begin{gathered} y+3=-x-6 \\ y=-x-9 \end{gathered}[/tex]Final answer:
y=x+3
y=-x-9
A basketball team has 13 Active players, in how many ways can 5 players be selected to start the game??
Answer:
1287
Explanation:
The number of distinct ways n objects can b selected from N total objects is given by
[tex]\frac{N!}{n!(N-n)!}[/tex]Now in our case, we have a total of 13 basketball players. N = 13 and 5 players to choose n = 5. Therefore, the above formula gives
[tex]\frac{13!}{5!(13-5)!}[/tex][tex]-\frac{13!}{5!8!}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{5!\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10}{5!}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10}{5\cdot4\cdot3\cdot2\cdot1}[/tex][tex]=1287[/tex]Hence, there are 1287 ways 5 different players can be selected from 13 players.
Which equation represents a line which is parallel to the line y = 1/3x +6x+3y=243y-x=-183y−x=−183x-y=73x−y=73x+y=-83x+y=−8
Recall that two lines are parallel if they have the same slope.
Now, the given equation is in the form
[tex]y=mx+b,[/tex]where m is the slope. Therefore, the slope of the given line is
[tex]\frac{1}{3},[/tex]and it has to be the slope of the parallel line.
Taking the options to their slope-intercept form, we can determine which equation represents a parallel line to the given line.
Answer: An equation of the form:
[tex]y=\frac{1}{3}x+b\text{.}[/tex]Where b is a constant.
A license plate has two letters followed by three digits.What is the probability that the license plate are all odd numbers?
The number plate has two letters and three digits
The probability that the license plate are all odd numbers will be ...........
The probability of that the three numbers are odd is 1 / 2 x 1 / 2 x 1 / 2 = 1/8
Supposed to go out to a dinner and you spend $42 you want to leave a 20% tip how much money should you leave for a tip round your answer to the nearest cent
Answer:
$8.4
Explanation:
To find how much money you should leave for a tip, we need to find how much is 20% of $42. So, to calculate this, we need to multiply 42 by 20 and then divide by 100, so:
$42 x 20% = 42 x 20 / 100 = 840 / 100 = 8.4
Therefore, the answer is $8.4
Solve using substitution. 6x + y = 5 -8x - 5y = 19 how do I do this
The given system of equations is
[tex]\begin{gathered} 6x+y=5 \\ -8x-5y=19 \end{gathered}[/tex]To solve the system, first, let's multiply the first equation by 5.
[tex]\begin{gathered} 30x+5y=25 \\ -8x-5y=19 \end{gathered}[/tex]Then, we combine the equations
[tex]\begin{gathered} 30x-8x+5y-5y=25+19 \\ 22x=44 \\ x=\frac{44}{22} \\ x=2 \end{gathered}[/tex]Now, we find y
[tex]\begin{gathered} 6x+y=5 \\ 6\cdot2+y=5 \\ 8+y=5 \\ y=5-8 \\ y=-3 \end{gathered}[/tex]Hence, the solution is (2,-3).Consider the graph of f(x) = 5 ^ x + 1 1. Explain how to find the average rate of change between x = 0 and x = 4 . What is the average rate of change ?
1. To determine the average rate of change of a function "f(x)" between the points "x = a" and "x = b" we use the following formula:
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]2. In this case, we have the following function:
[tex]f(x)=5^x+1[/tex]And we have the points:
[tex]\begin{gathered} x=0 \\ x=4 \end{gathered}[/tex]Now we determine the value of f(b) by replacing x = 4 in the function:
[tex]\begin{gathered} f(4)=5^4+1 \\ f(4)=626 \end{gathered}[/tex]Now we determine f(0):
[tex]\begin{gathered} f(0)=5^0+1 \\ f(0)=1+1=2 \end{gathered}[/tex]Replacing in the formula for the average rate of change we get:
[tex]A=\frac{626-2}{4-0}[/tex]Solving the operations:
[tex]A=\frac{624}{4}=156[/tex]Therefore, the average rate of change is 156.
write a linear equation that has m=4 and has an x intercept of (5,0)
the equation is of the form y = mx + b, then
for b:
[tex]\begin{gathered} 0=4(5)+b \\ 0=20+b \\ 0-20=20+b-20 \\ b=-20 \end{gathered}[/tex]the equation is:
[tex]y=4x-20[/tex]One type of dog treat, Barker, contains 3 oz and sells for $1.95. DogYum contains 3.25 and sells for $2.10.Which is less expensive, per ounce?A. DogYum is less expensive, per ounceB. Barker is less expensive, per ounce
Solution
- We are told that dog treats, Barker and DogYum cost $1.95 for 3 oz and $2.10 for 3.25 oz respectively and we are required to find out which is more expensive per ounce.
- In order to find the more expensive dog treat, we need to find the cost per ounce for each item. The cost per ounce is given by the formula below:
[tex]\frac{\text{Cost of dog treat (In Dollars)}}{\text{Weight of dog treat (In Oz)}}[/tex]- The dog treat with the larger cost per oz is the more expensive item.
- Thus, let us calculate the cost per oz for both items.
DogYum:
[tex]\begin{gathered} \frac{\text{Cost of DogYum}}{\text{Weight of DogYum}}=\frac{2.10}{3.25}=0.646 \\ \\ \text{Thus, the cost per oz of the DogYum treat is \$0.646/oz} \end{gathered}[/tex]Barker:
[tex]\begin{gathered} \frac{\text{ Cost of Barker}}{\text{Weight of Barker}}=\frac{1.95}{3}=0.65 \\ \\ \text{Thus, the cost per oz of the Barker treat is \$0.65/oz} \end{gathered}[/tex]- We can observe that Barker is marginally more expensive than DogYum. We can confirm this by simply subtracting the cost per oz for both treats.
[tex]\text{Barker - DogYum}=0.65-0.646=0.004[/tex]Final Answer
The answer is:
DogYum is less expensive, per ounce
Perform the indicated operation numbers be sure to express your answer in reduced form
We need to calculate the following sum:
[tex]\frac{8}{15}+\frac{7}{25}[/tex]The first step is to calculate the least common multiplier between the two denominators. This is done below:
[tex]\begin{gathered} 15=3\cdot5 \\ 25=5\cdot5 \end{gathered}[/tex]We broke down the two denominators into their factors, now we need to multiply the factors that are unique. This is done below:
[tex]\text{LCM}=3\cdot5\cdot5=75[/tex]Now we have to replace the denominators by 75 and calculate new numerators. The new numerators must be calculated as follows:
1 - Divide the LCM by the old denominator
2 - Multiply the result of 1 by the old numerator.
This is done below:
[tex]\begin{gathered} \frac{5\cdot8}{75}+\frac{3\cdot7}{75} \\ \frac{40}{75}+\frac{21}{75} \end{gathered}[/tex]Since both fractions have their denominators with the same value, we can just directly add them.
[tex]\frac{40+21}{75}=\frac{61}{75}[/tex]The fraction is already in its most reductable form, therefore the answer is 61/75.
tenemos $5000 en una cuenta. A final de cada mes se ingresa un 5% del dinero que hay en la cuenta en dicho momento. Calcular el dinero que habrá en la cuenta después de un trimestre¿ en que porcentaje ha subido la cantidad inicial?
Al final del primer mes tenemos:
5000 + 5000*0.05 = 5250
Al final del segundo mes:
5250 + 5250*0.05 = 5512.5
Y al final del tercer mes nos queda:
5512.5 + 5512.5*0.05 = 5788.125
El dinero que habra en la cuent despues de un trimestre es $5788.125
Para calcular en que porcentaje ha subido la cantidad inicial, dividimos la cantidad extra obtenida despues de un trimestre entre la cantidad inicial:
[tex]\begin{gathered} \frac{788.125}{5000}=0.157625 \\ \text{Expresado en porcentaje:} \\ 0.157625\cdot100=15.7625 \end{gathered}[/tex]Ha subido en un 15.7625%
Pls helpppp I don't know what 2×2 IS plsss
we have
2*2=2+2=4
5*5=5+5+5+5+.5=25
5 times 5
example
2*3
its 2 times 3
3+3=6
4*3
4 times 3
3+3+3+3=12
Answer:
2 x 2 = 4.
two multiplied by two equals four.
The distances between Centerville, Springfield, and Capital City form a right triangle. The distance between Centerville and Springfield is 913 kilometers and the distance between Springfield and Capital City is 976 kilometers. View the map.
Answer:
The distance between Centerville and Capital City is 1336 kilometers.
Step by step explanation:
To solve the situation, we can use the Pythagorean theorem, which is represented by the following expression and diagram:
Now, if a=913 kilometers and b=976 kilometers. Solve for c:
[tex]\begin{gathered} 913^2+976^2=c^2 \\ c=\sqrt[]{913^2+976^2} \\ c=\sqrt[]{833569+952576} \\ c=\sqrt[]{1786145} \\ c=1336\text{ kilometers} \end{gathered}[/tex]Find the value of tan X rounded to the nearest hundredth, if necessary.
5
W
1
√26
X
The value of tan x is 5
We need to find the value of tan x
Tan is one of the trignometric functions and the range of a tan function varies from 0 ≤ tan x ≤ 2π
In the triangle vwx, the perpendicular of x is VW and the base is WX
tan x = perpendicular / base
Here, the perependicular is 5 and base is 1
tan x = 5/1
tan x = 5
Therefore, the value of tan x is 5
To learn more about trignometric functions refer here
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Which of the following correctly shows the next two terms after -40 in the pattern?-10, 20, -40,...А.80, 160B-2.5,5С60, -80D80, -160
In the pattern -10,20,-40 every next term is obtained by multiplication of -2.
So terms next to -40 is,
[tex]-40\cdot(-2)=80[/tex]Term next to 80 is,
[tex]80\cdot(-2)=-160[/tex]Thus next two terms od -40 are 80 and -160.
Option D is correct option.
a. Use the line of random numbers to obtain and report the resulting list of heads and tails. Use H for heads and T for tails.Q0000 00.000 0.0.000 00000
Given -
An unbiased coin is tossed
To Find -
The list of heads and tails while tossing a coin
Assumption -
The coin is tossed twice
Explaination -
The following table lists some possible arrangements for the experiment
