Answer:
[tex]v\sqrt[28]{v^{13}}[/tex]
Step-by-step explanation:
The exponent rules that apply are ...
[tex](a^b)(a^c)=a^{b+c}\\\\a^{\frac{b}{c}}=\sqrt[c]{a^b}[/tex]
Using these rules for your product, we have ...
[tex]v^{\frac{3}{4}}\times v^{\frac{5}{7}}=v^{\frac{3}{4}+\frac{5}{7}}\\\\=v^{\frac{41}{28}}=v\cdot v^{\frac{13}{28}}=v\sqrt[28]{v^{13}}[/tex]
There are 70 campers and 6 instructors going to camp loon. If the vans hold 8 people,how many vans do they need?
They need about 9 vans.
Please help me
Find the mode of the following data set
The mode is the number that appears most often.
Looking at the chart, there are two 1's on the right side, so the mode would be 31
What are the solution of x^2-2x+17=0
Answer:
x = 1 - 4i or x = 1 + 4iStep-by-step explanation:
[tex]x^2-2x+17=0\qquad\text{subtract 17 from both sides}\\\\x^2-2x=-17\\\\x^2-2(x)(1)=-17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\x^2-2(x)(1)+1^2=-17+1^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-1)^2=-17+1\\\\(x-1)^2=-16<0\Rightarrow\boxed{\text{NO REAL SOLUTION}}\ because\ x^2\geq0\\\\\text{In the set of complex numbers}\\\\i=\sqrt{-1}\\\\(x-1)^2=-16\iff x-1=\pm\sqrt{-16}\\\\x-1=-\sqrt{(16)(-1)}\ \vee\ x-1=\sqrt{(16)(-1)}\\\\x-1=-\sqrt{16}\cdot\sqrt{-1}\ \vee\ x-1=\sqrt{16}\cdot\sqrt{-1)[/tex]
[tex]x-1=-4i\ \vee\ x-1=4i\qquad\text{add 1 to both sides}\\\\x=1-4i\ \vee\ x=1+4i[/tex]
Ello mates how are yall this fine time of day? what is 2+2?
Answer:
2+2 is 4
Step-by-step explanation:
Answer:
im doing just find what about you mate
Step-by-step explanation:the answer is 4
Write and equation of the translated or rotated graph in general form (picture below)
Answer:
Option b
Step-by-step explanation:
The equation [tex]4x ^ 2 + 5y ^ 2 = 20[/tex] has center in (0,0).
But the transformation [tex]T(5, -6)[/tex] shifts the center of the equation to the point (5, -6).
Therefore, when applying [tex]T(5, -6)[/tex] we will have the following equation translated.
[tex]4(x-5) ^ 2 + 5(y - (-6)) ^ 2 = 20[/tex].
Simplifying we have:
[tex]4(x-5) ^ 2 + 5(y + 6) ^ 2 = 20[/tex]
Now we expand [tex](x-5) ^ 2[/tex] and [tex](y + 6) ^ 2[/tex]
[tex]4(x ^ 2 -10x +25) + 5(y ^ 2 + 12y +36) = 20\\\\4x ^ 2 -40x + 100 + 5y ^ 2 + 60y + 180 = 20\\\\4x ^ 2 + 5y ^ 2 -40x + 60y +260 = 0[/tex]
The equation of a circle has the form
[tex]h(x-a) ^ 2 + q(y-b) ^ 2 = r[/tex]
For h = 1 and q = 1.
If [tex]h \neq 1[/tex] and [tex]q\neq 1[/tex] then the graph becomes an ellipse.
In this problem h = 4 and q = 5 therefore the figure is an ellipse
A bus travels 36 miles in 45 minutes. How many miles will it travel in 60 minutes at this rate?
Answer:
48 miles
Step-by-step explanation:
Rosa is painting two murals.The small mural has an.Area of 2.5 square meters.The Large mural has an area 1.5 times greater than the area of the small mural.What is the are of the large mural
Answer:
6.25 m²
Step-by-step explanation:
The area of the small mural is 1.5 times greater than that of the small mural.
That means the area of the large mural is 2.5 times the area of the small mural.
Area = 2.5 × 2.5 m² = 6.25 m²
The area of the large mural is 6.25 m².
For the given line segment, write the equation of the perpendicular bisector.
To find the equation of the perpendicular bisector, find the midpoint of the line segment and determine the slope of the perpendicular line.
Explanation:To find the equation of the perpendicular bisector of a given line segment, we need to find the midpoint of the segment and then determine the slope of the perpendicular line. Let's denote the coordinates of the endpoints of the line segment as (x1, y1) and (x2, y2). The midpoint of the segment can be found using the formula:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
The slope of the perpendicular line can be found using the negative reciprocal of the slope of the given line segment:
Perpendicular slope = -1 / slope of given line segment
Once we have the midpoint and the slope of the perpendicular line, we can use the point-slope form of a linear equation to write the equation of the perpendicular bisector:
y - y1 = perpendicular slope * (x - x1)
Suppose y = 2x + 1 , where x and y are functions of t. (a) if dx/dt = 3, find dy/dt when x = 4. dy dt = (b) if dy/dt = 2, find dx/dt when x = 40. dx dt =
Answer:
Step-by-step explanation:
If y = 2x + 1, then dy/dt = 2(dx/dt).
If y = 2x + 1, then y = 2(40) + 1 when 40 is substituted for x. y = 81.
(a) if dx/dt = 3, find dy/dt when x = 4:
Replacing dx/dt with 3 in dy/dt = 2(dx/dt) yields dy/dt = 2(3) = 6.
(b) if dy/dt = 2, find dx/dt when x = 40:
Replacing dy/dt with 2 in dy/dt = 2(dx/dt) results in 2 = 2(dx/dt), so dx/dt must be 1.
First, you differentiate the given function. Next, apply the chain rule which states dy/dt = dy/dx * dx/dt. Substitute the known values to find dy/dt. For the second part, rearrange the chain rule to find dx/dt = dy/dt / dy/dx and substitute the known values.
Explanation:This question deals with the basic application of the chain rule in differentiation. The given function is y = 2x + 1, where both y and x are functions of t. You are supposed to determine dy/dt and dx/dt.
(a) First, differentiate y = 2x + 1 with respect to x to obtain dy/dx = 2. According to the chain rule in calculus, dy/dt = dy/dx * dx/dt. Substituting the known values from the question, we have dy/dt = 2 * 3 = 6 when x = 4.
(b) For dy/dt = 2, you need to rearrange dy/dt = dy/dx * dx/dt to find dx/dt = dy/dt / dy/dx. As dy/dx = 2, you can evaluate dx/dt = 2 / 2 = 1 when x = 40.
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What is the volume of a sphere with a radius of 4 centimeters? (Use 3.14 for π.)
The volume of a sphere with a radius of 4 centimeters is calculated using the formula V = (4/3)πr³. Substituting 4 cm for the radius and 3.14 for π, the volume is approximately 268 cubic centimeters.
To calculate the volume of a sphere with a given radius, you can use the formula V = (4/3)πr³, where V represents the volume and r is the radius. In our case, the radius is 4 centimeters. Substituting the values into the formula gives us V = (4/3) * 3.14 * (4 cm)³.
Performing the calculation: V = (4/3) * 3.14 * 64 cm³ = 267.94666666666666 cm³. Therefore, the volume of the sphere is approximately 268 cm³ when rounded to a whole number.
Help please:
Find the product of (3x − 7y)2. (2 points)
9x2 − 42xy + 49y2
9x2 + 42xy + 49y2
9x2 − 49y2
9x2 + 49y2
The product of (3x - 7y)^2 is found by squaring the binomial using the FOIL method, which leads to 9x^2 - 42xy + 49y^2.
To find the product of (3x \\- 7y)^2, you must square the binomial. This means you will multiply the binomial by itself. When you square a binomial, you use the FOIL method (First, Outer, Inner, Last) to multiply the terms.
First: (3x)(3x) = 9x^2
Outer: (3x)(-7y) = -21xy
Inner: (-7y)(3x) = -21xy
Last: (-7y)(-7y) = 49y^2
Combine like terms (the Outer and Inner terms in this case).
9x^2 - 21xy - 21xy + 49y^2 = 9x^2 - 42xy + 49y^2
Thus, the product of (3x - 7y)^2 is 9x^2 - 42xy + 49y^2.
If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y, the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x?
Answer:
2nd graph
Step-by-step explanation:
Exponential increase will be a graph that increase all throughout and the rate of increase "increases" with age.
We can rule out first graph because if you draw smooth curve along the dots, it shows increase, then decrease.We can rule out third graph because it is increasing BUT not exponentially, rather, at a constant rate.We can rule out fourth graph because it is decreasing (exponentially).The 2nd graph is correct because it shown "increase" as well as "exponential" increase (the rate of increase increases).
Answer: 2nd graph
Your answer is going to be the second graph
find the area of the sector where the radius is 6 meters and the central angle is 78°
Answer:13
Step-by-step explanation:you have to divide it
The area of a sector is found using the formula :
Area = πr^2(angle/360)
R is given as 6 meters and the angle is given as 78 degrees.
Area = π * 6^2 * (78/360)
Area = π * 36 * 0.21666
Area = π * 7.8
Area = 7.8π square meters. ( Exact area in terms of PI)
or using 3.14 for PI: Area = 24.492 square meters.
Round the decimal area as needed.
7 is what percent of 20?
Solve this question without using any algebra (variables) and solely by using numbers
Decide if the function is an exponential function. If it is state the initial value and the base y=x^2
Answer:
B
Step-by-step explanation:
The exponential function is the function of the form
[tex]y=a\cdot b^x,[/tex]
where [tex]b[/tex] is the base and [tex]a[/tex] is the initial value.
The function [tex]y=x^2[/tex] is the quadratic function, which cannot be represented as [tex]y=a\cdot b^x.[/tex] Thus, this function is not exponential.
Answer:
The answer is B.
Step-by-step explanation:
Two more than a number is the same as 16 decreased by 6 times the number. Find the number .
Find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x → (π/2)+ cos x 1 − sin x
Looks like the limit is
[tex]\displaystyle\lim_{x\to\pi/2^+}\frac{\cos x}{1-\sin x}[/tex]
which yields an indeterminate form [tex]\dfrac00[/tex]. Rewriting as
[tex]\dfrac{\cos x(1+\sinx)}{(1-\sin x)(1+\sin x)}=\dfrac{\cos x(1+\sin x)}{1-\sin^2x}=\dfrac{1+\sin x}{\cos x}[/tex]
we see the numerator approaches 1 + 1 = 2, while the denominator approaches 0. Since [tex]\cos x<0[/tex] for [tex]x[/tex] near [tex]\dfrac\pi2[/tex] with [tex]x>\dfrac\pi2[/tex], the limit is [tex]-\infty[/tex].
An Olympic floor exercise mat has an area of 144 square meters. It's length is 12 meters.What is the shape of the mat?
Answer:
The shape of the mat is a square
Step-by-step explanation:
we know that
The area of the rectangle (An Olympic floor exercise mat) is equal to
[tex]A=LW[/tex]
we have that
[tex]A=144\ ft^{2}[/tex]
[tex]L=12\ ft[/tex]
substitute the values and solve for W
[tex]144=12W[/tex]
[tex]W=144/12=12\ ft[/tex]
so
The length is equal to the width
therefore
The shape of the mat is a square
i need hep with this ape question plz
Answer:
A
Step-by-step explanation:
The first "circle" is the "domain", which is the set of x values of the function.
The second "circle" is the "range", which is the set of y values of the function.
The range is 4, 7, 9. There are a few x values that match to same y-values but the range is basically the three numbers, 4, 7, and 9.
Option A, {4,7,9} is the correct answer.
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution. [You may find it useful to reference the t table.] a. Construct the 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to at least 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)
To construct a 90% confidence interval for the average number of customers who visit the salon on weekdays, calculate the sample mean and standard deviation, determine the critical t-value, and use the confidence interval formula to find the range.
Explanation:To construct a 90% confidence interval for the average number of customers who visit the salon on weekdays, we first calculate the sample mean and the sample standard deviation. The sample mean is the average of the seven data points (40, 30, 28, 22, 36, 16, and 50), which is 32. The sample standard deviation is the measure of variability in the data, which is calculated to be approximately 12.11.
Next, we determine the critical t-value for a 90% confidence interval with 6 degrees of freedom (7 data points minus 1). We can find this value in the t-distribution table or use statistical software, and it is approximately 1.943.
Finally, we can calculate the confidence interval using the formula: Confidence interval = sample mean ± (t-value * standard deviation / square root of sample size). Plugging in the values, we get the confidence interval as (23.52, 40.48). Therefore, we can be 90% confident that the average number of customers who visit the salon on weekdays falls within this range.
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If 10 boxes of 10 muffins each and each muffin has 10 blueberries use it exponent to write an expression for the total number of blueberries
Answer: [tex]b=10^3[/tex]
Step-by-step explanation:
You know that there are 10 blueberries in each muffin. There are 10 muffins in each box and the total number of boxes is 10.
Then, to calculate the total number of blueberries, you need to multiply the total number of boxes by the number of muffins in each box and multiply this by the number of blueberries in each muffin.
Let be "b" the total number of blueberries. Then:
[tex]b=10*10*10[/tex]
By the Product of powers property:
[tex]a^m*a^n=a^{(m+n)}[/tex]
Then you can write the expression:
[tex]b=10^3[/tex]
A community organization surveyed 40 members to determine if they world vote yes or no for the proposition a in the next election
Twelve of the surveyed members said they would vote yes there are a total of 240 members in the community organization how many members are expected to vote yes
Answer:
72 voters
Step-by-step explanation:
Total surveyed members: 40
Total members with a yes vote: 12
Percentage of the voters (voting yes): [tex]\frac{12}{40} * 100 = 30%[/tex]
From analysis, it is observed that 30% of the voters are expected to vote yes in a sample.
Therefore, the number of voters expected to vote yes out of 240 are: 30% of 240
=> [tex]\frac{30}{100} * 240 = 72[/tex]
Answer:
72 voters
Step-by-step explanation:
2x - y = 5 3x + 2y = 4 Solve the system of equations. A) (3, 1) B) (0, 2) C) (2, -1) D) ( 9 7 , 17 7 )
Solving the system of equation, we get Option (C) (2,-1).
How to solve the given set of equations ?The equations given are 2x - y = 5 and 3x + 2y = 4.
To find the point which solves the two equation, we have to satisfy the given x and y coordinates of the point on the given two equations.
Checking all the other Options, it does not satisfies except Option (C).
Checking the point (2,-1) on the first equation 2x - y = 5 , we get 5 in the left hand side of the equation.
Again checking the point (2,-1) on the second equation 3x + 2y = 4 , we get 4 in the left hand side of the equation.
Therefore the coordinates (2,-1) (Option C) satisfies both the equation which is the required solution.
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Vector u has a magnitude of 5 units, and vector v has a magnitude of 4 units. Which of these values are possible for the magnitude of u + v?
More than one answer is possible
A. 1
B. 9
C. 11
D. 13
Baily spends 3 hours each week playing soccer.This is two times the amount of time she spends working out in the weight room.How much time does she spend in the weight room each week?
A. 2w=3
B. 2+w=3
C. w=2.3
D. 3w=2
The correct equation representing the time Bailey spends in the weight room each week is 2w=3. By solving this equation, we find Bailey spends 1.5 hours in the weight room each week.
Explanation:The question tells us that Baily spends 3 hours each week playing soccer and this is two times the amount of time she spends working out in the weight room. We can represent the time she spends in the weight room as w. So, the question gives us the equation 2w=3. Since 2 times what number gives us 3, we can solve for w by dividing both sides of the equation by 2. When we do this, we have w=3/2, which means Baily spends 1.5 hours in the weight room each week.
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The value of [tex]\sqrt[3]{x}[/tex] where x is an integer, is located between 6 and 7 on the number line. What could be the value of x?
[tex]\displaystyle\\6<\sqrt[3]{x}<7~~~\Big|^3\\\\6^3<\Big(\sqrt[3]{x}\Big)^3<7^3\\\\216<x<343\\\\\boxed{x\in\{217,~218,~219,~220,~\cdots~,~340,~341,~342\}}[/tex]
.
Answer:
Step-by-step explanation:
The value would be 6.5
Write and equation of the translated or rotated graph in general form (picture below)
Answer:
The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
xy = -8
∵ A = 0 , B = 1 , C = 0
∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0
∴ B² - 4AC > 0
∴ The graph is hyperbola
* The equation xy = -8
∵ We have term xy that means we rotated the graph about
the origin by angle Ф
∵ Ф = π/4
∴ We rotated the x-axis and the y-axis by angle π/4
* That means the point (x' , y') it was point (x , y)
- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ
∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)
∴ x' = x/√2 - y/√2 = (x - y)/√2
∴ y' = x/√2 + y/√2 = (x + y)/√2
* Lets substitute x' and y' in the 1st answer
∵ (x')² - (y')² - 16 = 0
∴ [tex](\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=[/tex]
( [tex]\frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0[/tex]
* Lets open the bracket
∴ [tex]\frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0[/tex]
* Lets add the like terms
∴ [tex]\frac{-4xy}{2}-16=0[/tex]
* Simplify the fraction
∴ -2xy - 16 = 0
* Divide the equation by -2
∴ xy + 8 = 0
∴ xy = -8 ⇒ our equation
∴ Answer (a) is our answer
∴ The answer is hyperbola; (x')² - (y')² - 16 = 0
* Look at the graph:
- The black is the equation (x')² - (y')² - 16 = 0
- The purple is the equation xy = -8
- The red line is x'
- The blue line is y'
Answer:
a. hyperbola;
complete the square to determine the minimum or maximum value of the function defined by the expression -x^2-4x+15
[tex] - {x}^{2} - 4x + 15 \\ = - {x}^{2} - 4x - 4 + 15 + 4 \\ = - ( {x}^{2} + 4x + 4) + 19 \\ = \underbrace{- {(x + 2)}^{2}}_{ \leqslant 0} + 19 \\ \Rightarrow - {(x + 2)}^{2} + 19 \leqslant 19 \\ \Rightarrow Maximum \: value \: is \: 19 \: as \: x=-2
[/tex]
X-treme Sports has skateboards at a 24% discount. Find the sale price of a $384 skateboard using percent paid.
To find the sale price of a $384 skateboard with a 24% discount, convert the paid percentage to a decimal (76% to 0.76) and multiply with the original price, resulting in a sale price of $291.84.
Explanation:To calculate the sale price of a skateboard originally priced at $384 with a 24% discount, we first need to determine what percentage of the original price will actually be paid. Since the discount is 24%, that means 76% of the original price will be paid (100% - 24% = 76%). To convert this percentage to a decimal, we divide by 100, getting 0.76.
Next, we find the sale price by multiplying the original price by the decimal form of the percentage paid:
$384 × 0.76 = $291.84 as the sale price of the skateboard.
Calculate the weight of an individual who uses 69.75 g of protein based on the 0.45 factor. How much does he weigh? 31 lbs. 69.3 lbs. 70.2 lbs. 155 lbs.
Answer:
155 lbs.
Step-by-step explanation:
69.75 g of protein divided by 0.45= 155
Answer: He weighs 155 lbs.
Step-by-step explanation:
Since we have given that
Amount of protein he used = 69.75 g
Factor = 0.45
We need to find the weight of an individual.
So, Weight of an individual is given by
[tex]Weight\times factor=Protein\\\\Weight=\dfrac{Protein}{Factor}[/tex]
[tex]=\dfrac{69.75}{0.45}\\\\=155\ lbs[/tex]
Hence, he weighs 155 lbs.